Home » Physics » AP Physics 1 & 2 » Defining & Graphing Motion

Dan Fullerton

Dan Fullerton

Defining & Graphing Motion

Slide Duration:

Table of Contents

Section 1: Introduction
What is Physics?

7m 38s

Intro
0:00
Objectives
0:12
What is Physics?
0:31
What is Matter, Energy, and How to They Interact
0:55
Why?
0:58
Physics Answers the 'Why' Questions.
1:05
Matter
1:23
Matter
1:29
Mass
1:33
Inertial Mass
1:53
Gravitational Mass
2:12
A Spacecraft's Mass
2:58
Energy
3:37
Energy: The Ability or Capacity to Do Work
3:39
Work: The Process of Moving an Object
3:45
The Ability or Capacity to Move an Object
3:54
Mass-Energy Equivalence
4:51
Relationship Between Mass and Energy E=mc2
5:01
The Mass of An Object is Really a Measure of Its Energy
5:05
The Study of Everything
5:42
Introductory Course
6:19
Next Steps
7:15
Math Review

24m 12s

Intro
0:00
Outline
0:10
Objectives
0:28
Why Do We Need Units?
0:52
Need to Set Specific Standards for Our Measurements
1:01
Physicists Have Agreed to Use the Systeme International
1:24
The Systeme International
1:50
Based on Powers of 10
1:52
7 Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Kelvin, Mole
2:02
The Meter
2:18
Meter is a Measure of Length
2:20
Measurements Smaller than a Meter, Use: Centimeter, Millimeter, Micrometer, Nanometer
2:25
Measurements Larger Than a Meter, Use Kilometer
2:38
The Kilogram
2:46
Roughly Equivalent to 2.2 English Pounds
2:49
Grams, Milligrams
2:53
Megagram
2:59
Seconds
3:10
Base Unit of Time
3:12
Minute, Hour, Day
3:20
Milliseconds, Microseconds
3:33
Derived Units
3:41
Velocity
3:45
Acceleration
3:57
Force
4:04
Prefixes for Powers of 10
4:21
Converting Fundamental Units, Example 1
4:53
Converting Fundamental Units, Example 2
7:18
Two-Step Conversions, Example 1
8:24
Two-Step Conversions, Example 2
10:06
Derived Unit Conversions
11:29
Multi-Step Conversions
13:25
Metric Estimations
15:04
What are Significant Figures?
16:01
Represent a Manner of Showing Which Digits In a Number Are Known to Some Level of Certainty
16:03
Example
16:09
Measuring with Sig Figs
16:36
Rule 1
16:40
Rule 2
16:44
Rule 3
16:52
Reading Significant Figures
16:57
All Non-Zero Digits Are Significant
17:04
All Digits Between Non-Zero Digits Are Significant
17:07
Zeros to the Left of the Significant Digits
17:11
Zeros to the Right of the Significant Digits
17:16
Non-Zero Digits
17:21
Digits Between Non-Zeros Are Significant
17:45
Zeroes to the Right of the Sig Figs Are Significant
18:17
Why Scientific Notation?
18:36
Physical Measurements Vary Tremendously in Magnitude
18:38
Example
18:47
Scientific Notation in Practice
19:23
Example 1
19:28
Example 2
19:44
Using Scientific Notation
20:02
Show Your Value Using Correct Number of Significant Figures
20:05
Move the Decimal Point
20:09
Show Your Number Being Multiplied by 10 Raised to the Appropriate Power
20:14
Accuracy and Precision
20:23
Accuracy
20:36
Precision
20:41
Example 1: Scientific Notation w/ Sig Figs
21:48
Example 2: Scientific Notation - Compress
22:25
Example 3: Scientific Notation - Compress
23:07
Example 4: Scientific Notation - Expand
23:31
Vectors & Scalars

25m 5s

Intro
0:00
Objectives
0:05
Scalars
0:29
Definition of Scalar
0:39
Temperature, Mass, Time
0:45
Vectors
1:12
Vectors are Quantities That Have Magnitude and Direction
1:13
Represented by Arrows
1:31
Vector Representations
1:47
Graphical Vector Addition
2:42
Graphical Vector Subtraction
4:58
Vector Components
6:08
Angle of a Vector
8:22
Vector Notation
9:52
Example 1: Vector Components
14:30
Example 2: Vector Components
16:05
Example 3: Vector Magnitude
17:26
Example 4: Vector Addition
19:38
Example 5: Angle of a Vector
24:06
Section 2: Mechanics
Defining & Graphing Motion

30m 11s

Intro
0:00
Objectives
0:07
Position
0:40
An Object's Position Cab Be Assigned to a Variable on a Number Scale
0:43
Symbol for Position
1:07
Distance
1:13
When Position Changes, An Object Has Traveled Some Distance
1:14
Distance is Scalar and Measured in Meters
1:21
Example 1: Distance
1:34
Displacement
2:17
Displacement is a Vector Which Describes the Straight Line From Start to End Point
2:18
Measured in Meters
2:27
Example 2: Displacement
2:39
Average Speed
3:32
The Distance Traveled Divided by the Time Interval
3:33
Speed is a Scalar
3:47
Example 3: Average Speed
3:57
Average Velocity
4:37
The Displacement Divided by the Time Interval
4:38
Velocity is a Vector
4:53
Example 4: Average Velocity
5:06
Example 5: Chuck the Hungry Squirrel
5:55
Acceleration
8:02
Rate At Which Velocity Changes
8:13
Acceleration is a Vector
8:26
Example 6: Acceleration Problem
8:52
Average vs. Instantaneous
9:44
Average Values Take Into Account an Entire Time Interval
9:50
Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time
9:54
Example 7: Average Velocity
10:06
Particle Diagrams
11:57
Similar to the Effect of Oil Leak from a Car on the Pavement
11:59
Accelerating
13:03
Position-Time Graphs
14:17
Shows Position as a Function of Time
14:24
Slope of x-t Graph
15:08
Slope Gives You the Velocity
15:09
Negative Indicates Direction
16:27
Velocity-Time Graphs
16:45
Shows Velocity as a Function of Time
16:49
Area Under v-t Graphs
17:47
Area Under the V-T Graph Gives You Change in Displacement
17:48
Example 8: Slope of a v-t Graph
19:45
Acceleration-Time Graphs
21:44
Slope of the v-t Graph Gives You Acceleration
21:45
Area Under the a-t Graph Gives You an Object's Change in Velocity
22:24
Example 10: Motion Graphing
24:03
Example 11: v-t Graph
27:14
Example 12: Displacement From v-t Graph
28:14
Kinematic Equations

36m 13s

Intro
0:00
Objectives
0:07
Problem-Solving Toolbox
0:42
Graphs Are Not Always the Most Effective
0:47
Kinematic Equations Helps us Solve for Five Key Variables
0:56
Deriving the Kinematic Equations
1:29
Kinematic Equations
7:40
Problem Solving Steps
8:13
Label Your Horizontal or Vertical Motion
8:20
Choose a Direction as Positive
8:24
Create a Motion Analysis Table
8:33
Fill in Your Givens
8:42
Solve for Unknowns
8:45
Example 1: Horizontal Kinematics
8:51
Example 2: Vertical Kinematics
11:13
Example 3: 2 Step Problem
13:25
Example 4: Acceleration Problem
16:44
Example 5: Particle Diagrams
17:56
Example 6: Quadratic Solution
20:13
Free Fall
24:24
When the Only Force Acting on an Object is the Force of Gravity, the Motion is Free Fall
24:27
Air Resistance
24:51
Drop a Ball
24:56
Remove the Air from the Room
25:02
Analyze the Motion of Objects by Neglecting Air Resistance
25:06
Acceleration Due to Gravity
25:22
g = 9.8 m/s2
25:25
Approximate g as 10 m/s2 on the AP Exam
25:37
G is Referred to as the Gravitational Field Strength
25:48
Objects Falling From Rest
26:15
Objects Starting from Rest Have an Initial velocity of 0
26:19
Acceleration is +g
26:34
Example 7: Falling Objects
26:47
Objects Launched Upward
27:59
Acceleration is -g
28:04
At Highest Point, the Object has a Velocity of 0
28:19
Symmetry of Motion
28:27
Example 8: Ball Thrown Upward
28:47
Example 9: Height of a Jump
29:23
Example 10: Ball Thrown Downward
33:08
Example 11: Maximum Height
34:16
Projectiles

20m 32s

Intro
0:00
Objectives
0:06
What is a Projectile?
0:26
An Object That is Acted Upon Only By Gravity
0:29
Typically Launched at an Angle
0:43
Path of a Projectile
1:03
Projectiles Launched at an Angle Move in Parabolic Arcs
1:06
Symmetric and Parabolic
1:32
Horizontal Range and Max Height
1:49
Independence of Motion
2:17
Vertical
2:49
Horizontal
2:52
Example 1: Horizontal Launch
3:49
Example 2: Parabolic Path
7:41
Angled Projectiles
8:30
Must First Break Up the Object's Initial Velocity Into x- and y- Components of Initial Velocity
8:32
An Object Will Travel the Maximum Horizontal Distance with a Launch Angle of 45 Degrees
8:43
Example 3: Human Cannonball
8:55
Example 4: Motion Graphs
12:55
Example 5: Launch From a Height
15:33
Example 6: Acceleration of a Projectile
19:56
Relative Motion

10m 52s

Intro
0:00
Objectives
0:06
Reference Frames
0:18
Motion of an Observer
0:21
No Way to Distinguish Between Motion at Rest and Motion at a Constant Velocity
0:44
Motion is Relative
1:35
Example 1
1:39
Example 2
2:09
Calculating Relative Velocities
2:31
Example 1
2:43
Example 2
2:48
Example 3
2:52
Example 1
4:58
Example 2: Airspeed
6:19
Example 3: 2-D Relative Motion
7:39
Example 4: Relative Velocity with Direction
9:40
Newton's 1st Law of Motion

10m 16s

Intro
0:00
Objective
0:05
Newton's 1st Law of Motion
0:16
An Object At Rest Will Remain At Rest
0:21
An Object In Motion Will Remain in Motion
0:26
Net Force
0:39
Also Known As the Law of Inertia
0:46
Force
1:02
Push or Pull
1:04
Newtons
1:08
Contact and Field Forces
1:31
Contact Forces
1:50
Field Forces
2:11
What is a Net Force?
2:30
Vector Sum of All the Forces Acting on an Object
2:33
Translational Equilibrium
2:37
Unbalanced Force Is a Net Force
2:46
What Does It Mean?
3:49
An Object Will Continue in Its Current State of Motion Unless an Unbalanced Force Acts Upon It
3:50
Example of Newton's First Law
4:20
Objects in Motion
5:05
Will Remain in Motion At Constant Velocity
5:06
Hard to Find a Frictionless Environment on Earth
5:10
Static Equilibrium
5:40
Net Force on an Object is 0
5:44
Inertia
6:21
Tendency of an Object to Resist a Change in Velocity
6:23
Inertial Mass
6:35
Gravitational Mass
6:40
Example 1: Inertia
7:10
Example 2: Inertia
7:37
Example 3: Translational Equilibrium
8:03
Example 4: Net Force
8:40
Newton's 2nd Law of Motion

34m 55s

Intro
0:00
Objective
0:07
Free Body Diagrams
0:37
Tools Used to Analyze Physical Situations
0:40
Show All the Forces Acting on a Single Object
0:45
Drawing FBDs
0:58
Draw Object of Interest as a Dot
1:00
Sketch a Coordinate System
1:10
Example 1: Falling Elephant
1:18
Example 2: Falling Elephant with Air Resistance
2:07
Example 3: Soda on Table
3:00
Example 4: Box in Equilibrium
4:25
Example 5: Block on a Ramp
5:01
Pseudo-FBDs
5:53
Draw When Forces Don't Line Up with Axes
5:56
Break Forces That Don’t Line Up with Axes into Components That Do
6:00
Example 6: Objects on a Ramp
6:32
Example 7: Car on a Banked Turn
10:23
Newton's 2nd Law of Motion
12:56
The Acceleration of an Object is in the Direction of the Directly Proportional to the Net Force Applied
13:06
Newton's 1st Two Laws Compared
13:45
Newton's 1st Law
13:51
Newton's 2nd Law
14:10
Applying Newton's 2nd Law
14:50
Example 8: Applying Newton's 2nd Law
15:23
Example 9: Stopping a Baseball
16:52
Example 10: Block on a Surface
19:51
Example 11: Concurrent Forces
21:16
Mass vs. Weight
22:28
Mass
22:29
Weight
22:47
Example 12: Mass vs. Weight
23:16
Translational Equilibrium
24:47
Occurs When There Is No Net Force on an Object
24:49
Equilibrant
24:57
Example 13: Translational Equilibrium
25:29
Example 14: Translational Equilibrium
26:56
Example 15: Determining Acceleration
28:05
Example 16: Suspended Mass
31:03
Newton's 3rd Law of Motion

5m 58s

Intro
0:00
Objectives
0:06
Newton's 3rd Law of Motion
0:20
All Forces Come in Pairs
0:24
Examples
1:22
Action-Reaction Pairs
2:07
Girl Kicking Soccer Ball
2:11
Rocket Ship in Space
2:29
Gravity on You
2:53
Example 1: Force of Gravity
3:34
Example 2: Sailboat
4:00
Example 3: Hammer and Nail
4:49
Example 4: Net Force
5:06
Friction

17m 49s

Intro
0:00
Objectives
0:06
Examples
0:23
Friction Opposes Motion
0:24
Kinetic Friction
0:27
Static Friction
0:36
Magnitude of Frictional Force Is Determined By Two Things
0:41
Coefficient Friction
2:27
Ratio of the Frictional Force and the Normal Force
2:28
Chart of Different Values of Friction
2:48
Kinetic or Static?
3:31
Example 1: Car Sliding
4:18
Example 2: Block on Incline
5:03
Calculating the Force of Friction
5:48
Depends Only Upon the Nature of the Surfaces in Contact and the Magnitude of the Force
5:50
Terminal Velocity
6:14
Air Resistance
6:18
Terminal Velocity of the Falling Object
6:33
Example 3: Finding the Frictional Force
7:36
Example 4: Box on Wood Surface
9:13
Example 5: Static vs. Kinetic Friction
11:49
Example 6: Drag Force on Airplane
12:15
Example 7: Pulling a Sled
13:21
Dynamics Applications

35m 27s

Intro
0:00
Objectives
0:08
Free Body Diagrams
0:49
Drawing FBDs
1:09
Draw Object of Interest as a Dot
1:12
Sketch a Coordinate System
1:18
Example 1: FBD of Block on Ramp
1:39
Pseudo-FBDs
1:59
Draw Object of Interest as a Dot
2:00
Break Up the Forces
2:07
Box on a Ramp
2:12
Example 2: Box at Rest
4:28
Example 3: Box Held by Force
5:00
What is an Atwood Machine?
6:46
Two Objects are Connected by a Light String Over a Mass-less Pulley
6:49
Properties of Atwood Machines
7:13
Ideal Pulleys are Frictionless and Mass-less
7:16
Tension is Constant in a Light String Passing Over an Ideal Pulley
7:23
Solving Atwood Machine Problems
8:02
Alternate Solution
12:07
Analyze the System as a Whole
12:12
Elevators
14:24
Scales Read the Force They Exert on an Object Placed Upon Them
14:42
Can be Used to Analyze Using Newton's 2nd Law and Free body Diagrams
15:23
Example 4: Elevator Accelerates Upward
15:36
Example 5: Truck on a Hill
18:30
Example 6: Force Up a Ramp
19:28
Example 7: Acceleration Down a Ramp
21:56
Example 8: Basic Atwood Machine
24:05
Example 9: Masses and Pulley on a Table
26:47
Example 10: Mass and Pulley on a Ramp
29:15
Example 11: Elevator Accelerating Downward
33:00
Impulse & Momentum

26m 6s

Intro
0:00
Objectives
0:06
Momentum
0:31
Example
0:35
Momentum measures How Hard It Is to Stop a Moving Object
0:47
Vector Quantity
0:58
Example 1: Comparing Momenta
1:48
Example 2: Calculating Momentum
3:08
Example 3: Changing Momentum
3:50
Impulse
5:02
Change In Momentum
5:05
Example 4: Impulse
5:26
Example 5: Impulse-Momentum
6:41
Deriving the Impulse-Momentum Theorem
9:04
Impulse-Momentum Theorem
12:02
Example 6: Impulse-Momentum Theorem
12:15
Non-Constant Forces
13:55
Impulse or Change in Momentum
13:56
Determine the Impulse by Calculating the Area of the Triangle Under the Curve
14:07
Center of Mass
14:56
Real Objects Are More Complex Than Theoretical Particles
14:59
Treat Entire Object as if Its Entire Mass Were Contained at the Object's Center of Mass
15:09
To Calculate the Center of Mass
15:17
Example 7: Force on a Moving Object
15:49
Example 8: Motorcycle Accident
17:49
Example 9: Auto Collision
19:32
Example 10: Center of Mass (1D)
21:29
Example 11: Center of Mass (2D)
23:28
Collisions

21m 59s

Intro
0:00
Objectives
0:09
Conservation of Momentum
0:18
Linear Momentum is Conserved in an Isolated System
0:21
Useful for Analyzing Collisions and Explosions
0:27
Momentum Tables
0:58
Identify Objects in the System
1:05
Determine the Momenta of the Objects Before and After the Event
1:10
Add All the Momenta From Before the Event and Set Them Equal to Momenta After the Event
1:15
Solve Your Resulting Equation for Unknowns
1:20
Types of Collisions
1:31
Elastic Collision
1:36
Inelastic Collision
1:56
Example 1: Conservation of Momentum (1D)
2:02
Example 2: Inelastic Collision
5:12
Example 3: Recoil Velocity
7:16
Example 4: Conservation of Momentum (2D)
9:29
Example 5: Atomic Collision
16:02
Describing Circular Motion

7m 18s

Intro
0:00
Objectives
0:07
Uniform Circular Motion
0:20
Circumference
0:32
Average Speed Formula Still Applies
0:46
Frequency
1:03
Number of Revolutions or Cycles Which Occur Each Second
1:04
Hertz
1:24
Formula for Frequency
1:28
Period
1:36
Time It Takes for One Complete Revolution or Cycle
1:37
Frequency and Period
1:54
Example 1: Car on a Track
2:08
Example 2: Race Car
3:55
Example 3: Toy Train
4:45
Example 4: Round-A-Bout
5:39
Centripetal Acceleration & Force

26m 37s

Intro
0:00
Objectives
0:08
Uniform Circular Motion
0:38
Direction of ac
1:41
Magnitude of ac
3:50
Centripetal Force
4:08
For an Object to Accelerate, There Must Be a Net Force
4:18
Centripetal Force
4:26
Calculating Centripetal Force
6:14
Example 1: Acceleration
7:31
Example 2: Direction of ac
8:53
Example 3: Loss of Centripetal Force
9:19
Example 4: Velocity and Centripetal Force
10:08
Example 5: Demon Drop
10:55
Example 6: Centripetal Acceleration vs. Speed
14:11
Example 7: Calculating ac
15:03
Example 8: Running Back
15:45
Example 9: Car at an Intersection
17:15
Example 10: Bucket in Horizontal Circle
18:40
Example 11: Bucket in Vertical Circle
19:20
Example 12: Frictionless Banked Curve
21:55
Gravitation

32m 56s

Intro
0:00
Objectives
0:08
Universal Gravitation
0:29
The Bigger the Mass the Closer the Attraction
0:48
Formula for Gravitational Force
1:16
Calculating g
2:43
Mass of Earth
2:51
Radius of Earth
2:55
Inverse Square Relationship
4:32
Problem Solving Hints
7:21
Substitute Values in For Variables at the End of the Problem Only
7:26
Estimate the Order of Magnitude of the Answer Before Using Your Calculator
7:38
Make Sure Your Answer Makes Sense
7:55
Example 1: Asteroids
8:20
Example 2: Meteor and the Earth
10:17
Example 3: Satellite
13:13
Gravitational Fields
13:50
Gravity is a Non-Contact Force
13:54
Closer Objects
14:14
Denser Force Vectors
14:19
Gravitational Field Strength
15:09
Example 4: Astronaut
16:19
Gravitational Potential Energy
18:07
Two Masses Separated by Distance Exhibit an Attractive Force
18:11
Formula for Gravitational Field
19:21
How Do Orbits Work?
19:36
Example5: Gravitational Field Strength for Space Shuttle in Orbit
21:35
Example 6: Earth's Orbit
25:13
Example 7: Bowling Balls
27:25
Example 8: Freely Falling Object
28:07
Example 9: Finding g
28:40
Example 10: Space Vehicle on Mars
29:10
Example 11: Fg vs. Mass Graph
30:24
Example 12: Mass on Mars
31:14
Example 13: Two Satellites
31:51
Rotational Kinematics

15m 33s

Intro
0:00
Objectives
0:07
Radians and Degrees
0:26
In Degrees, Once Around a Circle is 360 Degrees
0:29
In Radians, Once Around a Circle is 2π
0:34
Example 1: Degrees to Radians
0:57
Example 2: Radians to Degrees
1:31
Linear vs. Angular Displacement
2:00
Linear Position
2:05
Angular Position
2:10
Linear vs. Angular Velocity
2:35
Linear Speed
2:39
Angular Speed
2:42
Direction of Angular Velocity
3:05
Converting Linear to Angular Velocity
4:22
Example 3: Angular Velocity Example
4:41
Linear vs. Angular Acceleration
5:36
Example 4: Angular Acceleration
6:15
Kinematic Variable Parallels
7:47
Displacement
7:52
Velocity
8:10
Acceleration
8:16
Time
8:22
Kinematic Variable Translations
8:30
Displacement
8:34
Velocity
8:42
Acceleration
8:50
Time
8:58
Kinematic Equation Parallels
9:09
Kinematic Equations
9:12
Delta
9:33
Final Velocity Squared and Angular Velocity Squared
9:54
Example 5: Medieval Flail
10:24
Example 6: CD Player
10:57
Example 7: Carousel
12:13
Example 8: Circular Saw
13:35
Torque

11m 21s

Intro
0:00
Objectives
0:05
Torque
0:18
Force That Causes an Object to Turn
0:22
Must be Perpendicular to the Displacement to Cause a Rotation
0:27
Lever Arm: The Stronger the Force, The More Torque
0:45
Direction of the Torque Vector
1:53
Perpendicular to the Position Vector and the Force Vector
1:54
Right-Hand Rule
2:08
Newton's 2nd Law: Translational vs. Rotational
2:46
Equilibrium
3:58
Static Equilibrium
4:01
Dynamic Equilibrium
4:09
Rotational Equilibrium
4:22
Example 1: Pirate Captain
4:32
Example 2: Auto Mechanic
5:25
Example 3: Sign Post
6:44
Example 4: See-Saw
9:01
Rotational Dynamics

36m 6s

Intro
0:00
Objectives
0:08
Types of Inertia
0:39
Inertial Mass (Translational Inertia)
0:42
Moment of Inertia (Rotational Inertia)
0:53
Moment of Inertia for Common Objects
1:48
Example 1: Calculating Moment of Inertia
2:53
Newton's 2nd Law - Revisited
5:09
Acceleration of an Object
5:15
Angular Acceleration of an Object
5:24
Example 2: Rotating Top
5:47
Example 3: Spinning Disc
7:54
Angular Momentum
9:41
Linear Momentum
9:43
Angular Momentum
10:00
Calculating Angular Momentum
10:51
Direction of the Angular Momentum Vector
11:26
Total Angular Momentum
12:29
Example 4: Angular Momentum of Particles
14:15
Example 5: Rotating Pedestal
16:51
Example 6: Rotating Discs
18:39
Angular Momentum and Heavenly Bodies
20:13
Types of Kinetic Energy
23:41
Objects Traveling with a Translational Velocity
23:45
Objects Traveling with Angular Velocity
24:00
Translational vs. Rotational Variables
24:33
Example 7: Kinetic Energy of a Basketball
25:45
Example 8: Playground Round-A-Bout
28:17
Example 9: The Ice Skater
30:54
Example 10: The Bowler
33:15
Work & Power

31m 20s

Intro
0:00
Objectives
0:09
What Is Work?
0:31
Power Output
0:35
Transfer Energy
0:39
Work is the Process of Moving an Object by Applying a Force
0:46
Examples of Work
0:56
Calculating Work
2:16
Only the Force in the Direction of the Displacement Counts
2:33
Formula for Work
2:48
Example 1: Moving a Refrigerator
3:16
Example 2: Liberating a Car
3:59
Example 3: Crate on a Ramp
5:20
Example 4: Lifting a Box
7:11
Example 5: Pulling a Wagon
8:38
Force vs. Displacement Graphs
9:33
The Area Under a Force vs. Displacement Graph is the Work Done by the Force
9:37
Find the Work Done
9:49
Example 6: Work From a Varying Force
11:00
Hooke's Law
12:42
The More You Stretch or Compress a Spring, The Greater the Force of the Spring
12:46
The Spring's Force is Opposite the Direction of Its Displacement from Equilibrium
13:00
Determining the Spring Constant
14:21
Work Done in Compressing the Spring
15:27
Example 7: Finding Spring Constant
16:21
Example 8: Calculating Spring Constant
17:58
Power
18:43
Work
18:46
Power
18:50
Example 9: Moving a Sofa
19:26
Calculating Power
20:41
Example 10: Motors Delivering Power
21:27
Example 11: Force on a Cyclist
22:40
Example 12: Work on a Spinning Mass
23:52
Example 13: Work Done by Friction
25:05
Example 14: Units of Power
28:38
Example 15: Frictional Force on a Sled
29:43
Energy

20m 15s

Intro
0:00
Objectives
0:07
What is Energy?
0:24
The Ability or Capacity to do Work
0:26
The Ability or Capacity to Move an Object
0:34
Types of Energy
0:39
Energy Transformations
2:07
Transfer Energy by Doing Work
2:12
Work-Energy Theorem
2:20
Units of Energy
2:51
Kinetic Energy
3:08
Energy of Motion
3:13
Ability or Capacity of a Moving Object to Move Another Object
3:17
A Single Object Can Only Have Kinetic Energy
3:46
Example 1: Kinetic Energy of a Motorcycle
5:08
Potential Energy
5:59
Energy An Object Possesses
6:10
Gravitational Potential Energy
7:21
Elastic Potential Energy
9:58
Internal Energy
10:16
Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration
10:20
Calculating Gravitational Potential Energy in a Constant Gravitational Field
10:57
Sources of Energy on Earth
12:41
Example 2: Potential Energy
13:41
Example 3: Energy of a System
14:40
Example 4: Kinetic and Potential Energy
15:36
Example 5: Pendulum
16:55
Conservation of Energy

23m 20s

Intro
0:00
Objectives
0:08
Law of Conservation of Energy
0:22
Energy Cannot Be Created or Destroyed.. It Can Only Be Changed
0:27
Mechanical Energy
0:34
Conservation Laws
0:40
Examples
0:49
Kinematics vs. Energy
4:34
Energy Approach
4:56
Kinematics Approach
6:04
The Pendulum
8:07
Example 1: Cart Compressing a Spring
13:09
Example 2
14:23
Example 3: Car Skidding to a Stop
16:15
Example 4: Accelerating an Object
17:27
Example 5: Block on Ramp
18:06
Example 6: Energy Transfers
19:21
Simple Harmonic Motion

58m 30s

Intro
0:00
Objectives
0:08
What Is Simple Harmonic Motion?
0:57
Nature's Typical Reaction to a Disturbance
1:00
A Displacement Which Results in a Linear Restoring Force Results in SHM
1:25
Review of Springs
1:43
When a Force is Applied to a Spring, the Spring Applies a Restoring Force
1:46
When the Spring is in Equilibrium, It Is 'Unstrained'
1:54
Factors Affecting the Force of A Spring
2:00
Oscillations
3:42
Repeated Motions
3:45
Cycle 1
3:52
Period
3:58
Frequency
4:07
Spring-Block Oscillator
4:47
Mass of the Block
4:59
Spring Constant
5:05
Example 1: Spring-Block Oscillator
6:30
Diagrams
8:07
Displacement
8:42
Velocity
8:57
Force
9:36
Acceleration
10:09
U
10:24
K
10:47
Example 2: Harmonic Oscillator Analysis
16:22
Circular Motion vs. SHM
23:26
Graphing SHM
25:52
Example 3: Position of an Oscillator
28:31
Vertical Spring-Block Oscillator
31:13
Example 4: Vertical Spring-Block Oscillator
34:26
Example 5: Bungee
36:39
The Pendulum
43:55
Mass Is Attached to a Light String That Swings Without Friction About the Vertical Equilibrium
44:04
Energy and the Simple Pendulum
44:58
Frequency and Period of a Pendulum
48:25
Period of an Ideal Pendulum
48:31
Assume Theta is Small
48:54
Example 6: The Pendulum
50:15
Example 7: Pendulum Clock
53:38
Example 8: Pendulum on the Moon
55:14
Example 9: Mass on a Spring
56:01
Section 3: Fluids
Density & Buoyancy

19m 48s

Intro
0:00
Objectives
0:09
Fluids
0:27
Fluid is Matter That Flows Under Pressure
0:31
Fluid Mechanics is the Study of Fluids
0:44
Density
0:57
Density is the Ratio of an Object's Mass to the Volume It Occupies
0:58
Less Dense Fluids
1:06
Less Dense Solids
1:09
Example 1: Density of Water
1:27
Example 2: Volume of Gold
2:19
Example 3: Floating
3:06
Buoyancy
3:54
Force Exerted by a Fluid on an Object, Opposing the Object's Weight
3:56
Buoyant Force Determined Using Archimedes Principle
4:03
Example 4: Buoyant Force
5:12
Example 5: Shark Tank
5:56
Example 6: Concrete Boat
7:47
Example 7: Apparent Mass
10:08
Example 8: Volume of a Submerged Cube
13:21
Example 9: Determining Density
15:37
Pressure & Pascal's Principle

18m 7s

Intro
0:00
Objectives
0:09
Pressure
0:25
Pressure is the Effect of a Force Acting Upon a Surface
0:27
Formula for Pressure
0:41
Force is Always Perpendicular to the Surface
0:50
Exerting Pressure
1:03
Fluids Exert Outward Pressure in All Directions on the Sides of Any Container Holding the Fluid
1:36
Earth's Atmosphere Exerts Pressure
1:42
Example 1: Pressure on Keyboard
2:17
Example 2: Sleepy Fisherman
3:03
Example 3: Scale on Planet Physica
4:12
Example 4: Ranking Pressures
5:00
Pressure on a Submerged Object
6:45
Pressure a Fluid Exerts on an Object Submerged in That Fluid
6:46
If There Is Atmosphere Above the Fluid
7:03
Example 5: Gauge Pressure Scuba Diving
7:27
Example 6: Absolute Pressure Scuba Diving
8:13
Pascal's Principle
8:51
Force Multiplication Using Pascal's Principle
9:24
Example 7: Barber's Chair
11:38
Example 8: Hydraulic Auto Lift
13:26
Example 9: Pressure on a Penny
14:41
Example 10: Depth in Fresh Water
16:39
Example 11: Absolute vs. Gauge Pressure
17:23
Continuity Equation for Fluids

7m

Intro
0:00
Objectives
0:08
Conservation of Mass for Fluid Flow
0:18
Law of Conservation of Mass for Fluids
0:21
Volume Flow Rate Remains Constant Throughout the Pipe
0:35
Volume Flow Rate
0:59
Quantified In Terms Of Volume Flow Rate
1:01
Area of Pipe x Velocity of Fluid
1:05
Must Be Constant Throughout Pipe
1:10
Example 1: Tapered Pipe
1:44
Example 2: Garden Hose
2:37
Example 3: Oil Pipeline
4:49
Example 4: Roots of Continuity Equation
6:16
Bernoulli's Principle

20m

Intro
0:00
Objectives
0:08
Bernoulli's Principle
0:21
Airplane Wings
0:35
Venturi Pump
1:56
Bernoulli's Equation
3:32
Example 1: Torricelli's Theorem
4:38
Example 2: Gauge Pressure
7:26
Example 3: Shower Pressure
8:16
Example 4: Water Fountain
12:29
Example 5: Elevated Cistern
15:26
Section 4: Thermal Physics
Temperature, Heat, & Thermal Expansion

24m 17s

Intro
0:00
Objectives
0:12
Thermal Physics
0:42
Explores the Internal Energy of Objects Due to the Motion of the Atoms and Molecules Comprising the Objects
0:46
Explores the Transfer of This Energy From Object to Object
0:53
Temperature
1:00
Thermal Energy Is Related to the Kinetic Energy of All the Particles Comprising the Object
1:03
The More Kinetic Energy of the Constituent Particles Have, The Greater the Object's Thermal Energy
1:12
Temperature and Phases of Matter
1:44
Solids
1:48
Liquids
1:56
Gases
2:02
Average Kinetic Energy and Temperature
2:16
Average Kinetic Energy
2:24
Boltzmann's Constant
2:29
Temperature Scales
3:06
Converting Temperatures
4:37
Heat
5:03
Transfer of Thermal Energy
5:06
Accomplished Through Collisions Which is Conduction
5:13
Methods of Heat Transfer
5:52
Conduction
5:59
Convection
6:19
Radiation
6:31
Quantifying Heat Transfer in Conduction
6:37
Rate of Heat Transfer is Measured in Watts
6:42
Thermal Conductivity
7:12
Example 1: Average Kinetic Energy
7:35
Example 2: Body Temperature
8:22
Example 3: Temperature of Space
9:30
Example 4: Temperature of the Sun
10:44
Example 5: Heat Transfer Through Window
11:38
Example 6: Heat Transfer Across a Rod
12:40
Thermal Expansion
14:18
When Objects Are Heated, They Tend to Expand
14:19
At Higher Temperatures, Objects Have Higher Average Kinetic Energies
14:24
At Higher Levels of Vibration, The Particles Are Not Bound As Tightly to Each Other
14:30
Linear Expansion
15:11
Amount a Material Expands is Characterized by the Material's Coefficient of Expansion
15:14
One-Dimensional Expansion -> Linear Coefficient of Expansion
15:20
Volumetric Expansion
15:38
Three-Dimensional Expansion -> Volumetric Coefficient of Expansion
15:45
Volumetric Coefficient of Expansion is Roughly Three Times the Linear Coefficient of Expansion
16:03
Coefficients of Thermal Expansion
16:24
Example 7: Contracting Railroad Tie
16:59
Example 8: Expansion of an Aluminum Rod
18:37
Example 9: Water Spilling Out of a Glass
20:18
Example 10: Average Kinetic Energy vs. Temperature
22:18
Example 11: Expansion of a Ring
23:07
Ideal Gases

24m 15s

Intro
0:00
Objectives
0:10
Ideal Gases
0:25
Gas Is Comprised of Many Particles Moving Randomly in a Container
0:34
Particles Are Far Apart From One Another
0:46
Particles Do Not Exert Forces Upon One Another Unless They Come In Contact in an Elastic Collision
0:53
Ideal Gas Law
1:18
Atoms, Molecules, and Moles
2:56
Protons
2:59
Neutrons
3:15
Electrons
3:18
Examples
3:25
Example 1: Counting Moles
4:58
Example 2: Moles of CO2 in a Bottle
6:00
Example 3: Pressurized CO2
6:54
Example 4: Helium Balloon
8:53
Internal Energy of an Ideal Gas
10:17
The Average Kinetic Energy of the Particles of an Ideal Gas
10:21
Total Internal Energy of the Ideal Gas Can Be Found by Multiplying the Average Kinetic Energy of the Gas's Particles by the Numbers of Particles in the Gas
10:32
Example 5: Internal Energy of Oxygen
12:00
Example 6: Temperature of Argon
12:41
Root-Mean-Square Velocity
13:40
This is the Square Root of the Average Velocity Squared For All the Molecules in the System
13:43
Derived from the Maxwell-Boltzmann Distribution Function
13:56
Calculating vrms
14:56
Example 7: Average Velocity of a Gas
18:32
Example 8: Average Velocity of a Gas
19:44
Example 9: vrms of Molecules in Equilibrium
20:59
Example 10: Moles to Molecules
22:25
Example 11: Relating Temperature and Internal Energy
23:22
Thermodynamics

22m 29s

Intro
0:00
Objectives
0:06
Zeroth Law of Thermodynamics
0:26
First Law of Thermodynamics
1:00
The Change in the Internal Energy of a Closed System is Equal to the Heat Added to the System Plus the Work Done on the System
1:04
It is a Restatement of the Law of Conservation of Energy
1:19
Sign Conventions Are Important
1:25
Work Done on a Gas
1:44
Example 1: Adding Heat to a System
3:25
Example 2: Expanding a Gas
4:07
P-V Diagrams
5:11
Pressure-Volume Diagrams are Useful Tools for Visualizing Thermodynamic Processes of Gases
5:13
Use Ideal Gas Law to Determine Temperature of Gas
5:25
P-V Diagrams II
5:55
Volume Increases, Pressure Decreases
6:00
As Volume Expands, Gas Does Work
6:19
Temperature Rises as You Travel Up and Right on a PV Diagram
6:29
Example 3: PV Diagram Analysis
6:40
Types of PV Processes
7:52
Adiabatic
8:03
Isobaric
8:19
Isochoric
8:28
Isothermal
8:35
Adiabatic Processes
8:47
Heat Is not Transferred Into or Out of The System
8:50
Heat = 0
8:55
Isobaric Processes
9:19
Pressure Remains Constant
9:21
PV Diagram Shows a Horizontal Line
9:27
Isochoric Processes
9:51
Volume Remains Constant
9:52
PV Diagram Shows a Vertical Line
9:58
Work Done on the Gas is Zero
10:01
Isothermal Processes
10:27
Temperature Remains Constant
10:29
Lines on a PV Diagram Are Isotherms
10:31
PV Remains Constant
10:38
Internal Energy of Gas Remains Constant
10:40
Example 4: Adiabatic Expansion
10:46
Example 5: Removing Heat
11:25
Example 6: Ranking Processes
13:08
Second Law of Thermodynamics
13:59
Heat Flows Naturally From a Warmer Object to a Colder Object
14:02
Heat Energy Cannot be Completely Transformed Into Mechanical Work
14:11
All Natural Systems Tend Toward a Higher Level of Disorder
14:19
Heat Engines
14:52
Heat Engines Convert Heat Into Mechanical Work
14:56
Efficiency of a Heat Engine is the Ratio of the Engine You Get Out to the Energy You Put In
14:59
Power in Heat Engines
16:09
Heat Engines and PV Diagrams
17:38
Carnot Engine
17:54
It Is a Theoretical Heat Engine That Operates at Maximum Possible Efficiency
18:02
It Uses Only Isothermal and Adiabatic Processes
18:08
Carnot's Theorem
18:11
Example 7: Carnot Engine
18:49
Example 8: Maximum Efficiency
21:02
Example 9: PV Processes
21:51
Section 5: Electricity & Magnetism
Electric Fields & Forces

38m 24s

Intro
0:00
Objectives
0:10
Electric Charges
0:34
Matter is Made Up of Atoms
0:37
Protons Have a Charge of +1
0:45
Electrons Have a Charge of -1
1:00
Most Atoms Are Neutral
1:04
Ions
1:15
Fundamental Unit of Charge is the Coulomb
1:29
Like Charges Repel, While Opposites Attract
1:50
Example 1: Charge on an Object
2:22
Example 2: Charge of an Alpha Particle
3:36
Conductors and Insulators
4:27
Conductors Allow Electric Charges to Move Freely
4:30
Insulators Do Not Allow Electric Charges to Move Freely
4:39
Resistivity is a Material Property
4:45
Charging by Conduction
5:05
Materials May Be Charged by Contact, Known as Conduction
5:07
Conductors May Be Charged by Contact
5:24
Example 3: Charging by Conduction
5:38
The Electroscope
6:44
Charging by Induction
8:00
Example 4: Electrostatic Attraction
9:23
Coulomb's Law
11:46
Charged Objects Apply a Force Upon Each Other = Coulombic Force
11:52
Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges
12:04
Example 5: Determine Electrostatic Force
13:09
Example 6: Deflecting an Electron Beam
15:35
Electric Fields
16:28
The Property of Space That Allows a Charged Object to Feel a Force
16:44
Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge
17:01
The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force
17:24
Example 7: Field Between Metal Plates
17:58
Visualizing the Electric Field
19:27
Electric Field Lines Point Away from Positive Charges and Toward Negative Charges
19:40
Electric Field Lines Intersect Conductors at Right Angles to the Surface
19:50
Field Strength and Line Density Decreases as You Move Away From the Charges
19:58
Electric Field Lines
20:09
E Field Due to a Point Charge
22:32
Electric Fields Are Caused by Charges
22:35
Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law
22:38
To Find the Electric Field Due to Multiple Charges
23:09
Comparing Electricity to Gravity
23:56
Force
24:02
Field Strength
24:16
Constant
24:37
Charge/ Mass Units
25:01
Example 8: E Field From 3 Point Charges
25:07
Example 9: Where is the E Field Zero?
31:43
Example 10: Gravity and Electricity
36:38
Example 11: Field Due to Point Charge
37:34
Electric Potential Difference

35m 58s

Intro
0:00
Objectives
0:09
Electric Potential Energy
0:32
When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done
0:35
When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done
0:43
Electric Potential Difference
1:30
Example 1: Charge From Work
2:06
Example 2: Electric Energy
3:09
The Electron-Volt
4:02
Electronvolt (eV)
4:15
1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:28
Example 3: Energy in eV
5:33
Equipotential Lines
6:32
Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential
6:36
Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines
6:57
Drawing Equipotential Lines
8:15
Potential Due to a Point Charge
10:46
Calculate the Electric Field Vector Due to a Point Charge
10:52
Calculate the Potential Difference Due to a Point Charge
11:05
To Find the Potential Difference Due to Multiple Point Charges
11:16
Example 4: Potential Due to a Point Charge
11:52
Example 5: Potential Due to Point Charges
13:04
Parallel Plates
16:34
Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other
16:37
These Can Create a Capacitor
16:45
E Field Due to Parallel Plates
17:14
Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant
17:15
Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation
17:47
Capacitors
18:09
Electric Device Used to Store Charge
18:11
Once the Plates Are Charged, They Are Disconnected
18:30
Device's Capacitance
18:46
Capacitors Store Energy
19:28
Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other
19:31
Example 6: Capacitance
20:28
Example 7: Charge on a Capacitor
22:03
Designing Capacitors
24:00
Area of the Plates
24:05
Separation of the Plates
24:09
Insulating Material
24:13
Example 8: Designing a Capacitor
25:35
Example 9: Calculating Capacitance
27:39
Example 10: Electron in Space
29:47
Example 11: Proton Energy Transfer
30:35
Example 12: Two Conducting Spheres
32:50
Example 13: Equipotential Lines for a Capacitor
34:48
Current & Resistance

21m 14s

Intro
0:00
Objectives
0:06
Electric Current
0:19
Path Through Current Flows
0:21
Current is the Amount of Charge Passing a Point Per Unit Time
0:25
Conventional Current is the Direction of Positive Charge Flow
0:43
Example 1: Current Through a Resistor
1:19
Example 2: Current Due to Elementary Charges
1:47
Example 3: Charge in a Light Bulb
2:35
Example 4: Flashlights
3:03
Conductivity and Resistivity
4:41
Conductivity is a Material's Ability to Conduct Electric Charge
4:53
Resistivity is a Material's Ability to Resist the Movement of Electric Charge
5:11
Resistance vs. Resistivity vs. Resistors
5:35
Resistivity Is a Material Property
5:40
Resistance Is a Functional Property of an Element in an Electric Circuit
5:57
A Resistor is a Circuit Element
7:23
Resistors
7:45
Example 5: Calculating Resistance
8:17
Example 6: Resistance Dependencies
10:09
Configuration of Resistors
10:50
When Placed in a Circuit, Resistors Can be Organized in Both Serial and Parallel Arrangements
10:53
May Be Useful to Determine an Equivalent Resistance Which Could Be Used to Replace a System or Resistors with a Single Equivalent Resistor
10:58
Resistors in Series
11:15
Resistors in Parallel
12:35
Example 7: Finding Equivalent Resistance
15:01
Example 8: Length and Resistance
17:43
Example 9: Comparing Resistors
18:21
Example 10: Comparing Wires
19:12
Ohm's Law & Power

10m 35s

Intro
0:00
Objectives
0:06
Ohm's Law
0:21
Relates Resistance, Potential Difference, and Current Flow
0:23
Example 1: Resistance of a Wire
1:22
Example 2: Circuit Current
1:58
Example 3: Variable Resistor
2:30
Ohm's 'Law'?
3:22
Very Useful Empirical Relationship
3:31
Test if a Material is 'Ohmic'
3:40
Example 4: Ohmic Material
3:58
Electrical Power
4:24
Current Flowing Through a Circuit Causes a Transfer of Energy Into Different Types
4:26
Example: Light Bulb
4:36
Example: Television
4:58
Calculating Power
5:09
Electrical Energy
5:14
Charge Per Unit Time Is Current
5:29
Expand Using Ohm's Law
5:48
Example 5: Toaster
7:43
Example 6: Electric Iron
8:19
Example 7: Power of a Resistor
9:19
Example 8: Information Required to Determine Power in a Resistor
9:55
Circuits & Electrical Meters

8m 44s

Intro
0:00
Objectives
0:08
Electrical Circuits
0:21
A Closed-Loop Path Through Which Current Can Flow
0:22
Can Be Made Up of Most Any Materials, But Typically Comprised of Electrical Devices
0:27
Circuit Schematics
1:09
Symbols Represent Circuit Elements
1:30
Lines Represent Wires
1:33
Sources for Potential Difference: Voltaic Cells, Batteries, Power Supplies
1:36
Complete Conducting Paths
2:43
Voltmeters
3:20
Measure the Potential Difference Between Two Points in a Circuit
3:21
Connected in Parallel with the Element to be Measured
3:25
Have Very High Resistance
3:59
Ammeters
4:19
Measure the Current Flowing Through an Element of a Circuit
4:20
Connected in Series with the Circuit
4:25
Have Very Low Resistance
4:45
Example 1: Ammeter and Voltmeter Placement
4:56
Example 2: Analyzing R
6:27
Example 3: Voltmeter Placement
7:12
Example 4: Behavior or Electrical Meters
7:31
Circuit Analysis

48m 58s

Intro
0:00
Objectives
0:07
Series Circuits
0:27
Series Circuits Have Only a Single Current Path
0:29
Removal of any Circuit Element Causes an Open Circuit
0:31
Kirchhoff's Laws
1:36
Tools Utilized in Analyzing Circuits
1:42
Kirchhoff's Current Law States
1:47
Junction Rule
2:00
Kirchhoff's Voltage Law States
2:05
Loop Rule
2:18
Example 1: Voltage Across a Resistor
2:23
Example 2: Current at a Node
3:45
Basic Series Circuit Analysis
4:53
Example 3: Current in a Series Circuit
9:21
Example 4: Energy Expenditure in a Series Circuit
10:14
Example 5: Analysis of a Series Circuit
12:07
Example 6: Voltmeter In a Series Circuit
14:57
Parallel Circuits
17:11
Parallel Circuits Have Multiple Current Paths
17:13
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
17:15
Basic Parallel Circuit Analysis
18:19
Example 7: Parallel Circuit Analysis
21:05
Example 8: Equivalent Resistance
22:39
Example 9: Four Parallel Resistors
23:16
Example 10: Ammeter in a Parallel Circuit
26:27
Combination Series-Parallel Circuits
28:50
Look For Portions of the Circuit With Parallel Elements
28:56
Work Back to Original Circuit
29:09
Analysis of a Combination Circuit
29:20
Internal Resistance
34:11
In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'
34:16
Terminal Voltage of the Voltage Source is Reduced Slightly
34:25
Example 11: Two Voltage Sources
35:16
Example 12: Internal Resistance
42:46
Example 13: Complex Circuit with Meters
45:22
Example 14: Parallel Equivalent Resistance
48:24
RC Circuits

24m 47s

Intro
0:00
Objectives
0:08
Capacitors in Parallel
0:34
Capacitors Store Charge on Their Plates
0:37
Capacitors In Parallel Can Be Replaced with an Equivalent Capacitor
0:46
Capacitors in Series
2:42
Charge on Capacitors Must Be the Same
2:44
Capacitor In Series Can Be Replaced With an Equivalent Capacitor
2:47
RC Circuits
5:40
Comprised of a Source of Potential Difference, a Resistor Network, and One or More Capacitors
5:42
Uncharged Capacitors Act Like Wires
6:04
Charged Capacitors Act Like Opens
6:12
Charging an RC Circuit
6:23
Discharging an RC Circuit
11:36
Example 1: RC Analysis
14:50
Example 2: More RC Analysis
18:26
Example 3: Equivalent Capacitance
21:19
Example 4: More Equivalent Capacitance
22:48
Magnetic Fields & Properties

19m 48s

Intro
0:00
Objectives
0:07
Magnetism
0:32
A Force Caused by Moving Charges
0:34
Magnetic Domains Are Clusters of Atoms with Electrons Spinning in the Same Direction
0:51
Example 1: Types of Fields
1:23
Magnetic Field Lines
2:25
Make Closed Loops and Run From North to South Outside the Magnet
2:26
Magnetic Flux
2:42
Show the Direction the North Pole of a Magnet Would Tend to Point If Placed in the Field
2:54
Example 2: Lines of Magnetic Force
3:49
Example 3: Forces Between Bar Magnets
4:39
The Compass
5:28
The Earth is a Giant Magnet
5:31
The Earth's Magnetic North pole is Located Near the Geographic South Pole, and Vice Versa
5:33
A Compass Lines Up with the Net Magnetic Field
6:07
Example 3: Compass in Magnetic Field
6:41
Example 4: Compass Near a Bar Magnet
7:14
Magnetic Permeability
7:59
The Ratio of the Magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
8:02
Free Space
8:13
Highly Magnetic Materials Have Higher Values of Magnetic Permeability
8:34
Magnetic Dipole Moment
8:41
The Force That a Magnet Can Exert on Moving Charges
8:46
Relative Strength of a Magnet
8:54
Forces on Moving Charges
9:10
Moving Charges Create Magnetic Fields
9:11
Magnetic Fields Exert Forces on Moving Charges
9:17
Direction of the Magnetic Force
9:57
Direction is Given by the Right-Hand Rule
10:05
Right-Hand Rule
10:09
Mass Spectrometer
10:52
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
10:58
Used to Determine the Mass of an Unknown Particle
11:04
Velocity Selector
12:44
Mass Spectrometer with an Electric Field Added
12:47
Example 5: Force on an Electron
14:13
Example 6: Velocity of a Charged Particle
15:25
Example 7: Direction of the Magnetic Force
16:52
Example 8: Direction of Magnetic Force on Moving Charges
17:43
Example 9: Electron Released From Rest in Magnetic Field
18:53
Current-Carrying Wires

21m 29s

Intro
0:00
Objectives
0:09
Force on a Current-Carrying Wire
0:30
A Current-Carrying Wire in a Magnetic Field May Experience a Magnetic Force
0:33
Direction Given by the Right-Hand Rule
1:11
Example 1: Force on a Current-Carrying Wire
1:38
Example 2: Equilibrium on a Submerged Wire
2:33
Example 3: Torque on a Loop of Wire
5:55
Magnetic Field Due to a Current-Carrying Wire
8:49
Moving Charges Create Magnetic Fields
8:53
Wires Carry Moving Charges
8:56
Direction Given by the Right-Hand Rule
9:21
Example 4: Magnetic Field Due to a Wire
10:56
Magnetic Field Due to a Solenoid
12:12
Solenoid is a Coil of Wire
12:19
Direction Given by the Right-Hand Rule
12:47
Forces on 2 Parallel Wires
13:34
Current Flowing in the Same Direction
14:52
Current Flowing in Opposite Directions
14:57
Example 5: Magnetic Field Due to Wires
15:19
Example 6: Strength of an Electromagnet
18:35
Example 7: Force on a Wire
19:30
Example 8: Force Between Parallel Wires
20:47
Intro to Electromagnetic Induction

17m 26s

Intro
0:00
Objectives
0:09
Induced EMF
0:42
Charges Flowing Through a Wire Create Magnetic Fields
0:45
Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
0:49
Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
0:57
Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
1:17
Finding the Magnetic Flux
1:36
Magnetic Field Strength
1:39
Angle Between the Magnetic Field Strength and the Normal to the Area
1:51
Calculating Induced EMF
3:01
The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux
3:04
Induced EMF in a Rectangular Loop of Wire
4:03
Lenz's Law
5:17
Electric Generators and Motors
9:28
Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field
9:31
Generators Use Mechanical Energy to Turn the Coil of Wire
9:39
Electric Motor Operates Using Same Principle
10:30
Example 1: Finding Magnetic Flux
10:43
Example 2: Finding Induced EMF
11:54
Example 3: Changing Magnetic Field
13:52
Example 4: Current Induced in a Rectangular Loop of Wire
15:23
Section 6: Waves & Optics
Wave Characteristics

26m 41s

Intro
0:00
Objectives
0:09
Waves
0:32
Pulse
1:00
A Pulse is a Single Disturbance Which Carries Energy Through a Medium or Space
1:05
A Wave is a Series of Pulses
1:18
When a Pulse Reaches a Hard Boundary
1:37
When a Pulse Reaches a Soft or Flexible Boundary
2:04
Types of Waves
2:44
Mechanical Waves
2:56
Electromagnetic Waves
3:14
Types of Wave Motion
3:38
Longitudinal Waves
3:39
Transverse Waves
4:18
Anatomy of a Transverse Wave
5:18
Example 1: Waves Requiring a Medium
6:59
Example 2: Direction of Displacement
7:36
Example 3: Bell in a Vacuum Jar
8:47
Anatomy of a Longitudinal Wave
9:22
Example 4: Tuning Fork
9:57
Example 5: Amplitude of a Sound Wave
10:24
Frequency and Period
10:47
Example 6: Period of an EM Wave
11:23
Example 7: Frequency and Period
12:01
The Wave Equation
12:32
Velocity of a Wave is a Function of the Type of Wave and the Medium It Travels Through
12:36
Speed of a Wave is Related to Its Frequency and Wavelength
12:41
Example 8: Wavelength Using the Wave Equation
13:54
Example 9: Period of an EM Wave
14:35
Example 10: Blue Whale Waves
16:03
Sound Waves
17:29
Sound is a Mechanical Wave Observed by Detecting Vibrations in the Inner Ear
17:33
Particles of Sound Wave Vibrate Parallel With the Direction of the Wave's Velocity
17:56
Example 11: Distance from Speakers
18:24
Resonance
19:45
An Object with the Same 'Natural Frequency' May Begin to Vibrate at This Frequency
19:55
Classic Example
20:01
Example 12: Vibrating Car
20:32
Example 13: Sonar Signal
21:28
Example 14: Waves Across Media
24:06
Example 15: Wavelength of Middle C
25:24
Wave Interference

20m 45s

Intro
0:00
Objectives
0:09
Superposition
0:30
When More Than One Wave Travels Through the Same Location in the Same Medium
0:32
The Total Displacement is the Sum of All the Individual Displacements of the Waves
0:46
Example 1: Superposition of Pulses
1:01
Types of Interference
2:02
Constructive Interference
2:05
Destructive Interference
2:18
Example 2: Interference
2:47
Example 3: Shallow Water Waves
3:27
Standing Waves
4:23
When Waves of the Same Frequency and Amplitude Traveling in Opposite Directions Meet in the Same Medium
4:26
A Wave in Which Nodes Appear to be Standing Still and Antinodes Vibrate with Maximum Amplitude Above and Below the Axis
4:35
Standing Waves in String Instruments
5:36
Standing Waves in Open Tubes
8:49
Standing Waves in Closed Tubes
9:57
Interference From Multiple Sources
11:43
Constructive
11:55
Destructive
12:14
Beats
12:49
Two Sound Waves with Almost the Same Frequency Interfere to Create a Beat Pattern
12:52
A Frequency Difference of 1 to 4 Hz is Best for Human Detection of Beat Phenomena
13:05
Example 4
14:13
Example 5
18:03
Example 6
19:14
Example 7: Superposition
20:08
Wave Phenomena

19m 2s

Intro
0:00
Objective
0:08
Doppler Effect
0:36
The Shift In A Wave's Observed Frequency Due to Relative Motion Between the Source of the Wave and Observer
0:39
When Source and/or Observer Move Toward Each Other
0:45
When Source and/or Observer Move Away From Each Other
0:52
Practical Doppler Effect
1:01
Vehicle Traveling Past You
1:05
Applications Are Numerous and Widespread
1:56
Doppler Effect - Astronomy
2:43
Observed Frequencies Are Slightly Lower Than Scientists Would Predict
2:50
More Distant Celestial Objects Are Moving Away from the Earth Faster Than Nearer Objects
3:22
Example 1: Car Horn
3:36
Example 2: Moving Speaker
4:13
Diffraction
5:35
The Bending of Waves Around Obstacles
5:37
Most Apparent When Wavelength Is Same Order of Magnitude as the Obstacle/ Opening
6:10
Single-Slit Diffraction
6:16
Double-Slit Diffraction
8:13
Diffraction Grating
11:07
Sharper and Brighter Maxima
11:46
Useful for Determining Wavelengths Accurately
12:07
Example 3: Double Slit Pattern
12:30
Example 4: Determining Wavelength
16:05
Example 5: Radar Gun
18:04
Example 6: Red Shift
18:29
Light As a Wave

11m 35s

Intro
0:00
Objectives
0:14
Electromagnetic (EM) Waves
0:31
Light is an EM Wave
0:43
EM Waves Are Transverse Due to the Modulation of the Electric and Magnetic Fields Perpendicular to the Wave Velocity
1:00
Electromagnetic Wave Characteristics
1:37
The Product of an EM Wave's Frequency and Wavelength Must be Constant in a Vacuum
1:43
Polarization
3:36
Unpoloarized EM Waves Exhibit Modulation in All Directions
3:47
Polarized Light Consists of Light Vibrating in a Single Direction
4:07
Polarizers
4:29
Materials Which Act Like Filters to Only Allow Specific Polarizations of Light to Pass
4:33
Polarizers Typically Are Sheets of Material in Which Long Molecules Are Lined Up Like a Picket Fence
5:10
Polarizing Sunglasses
5:22
Reduce Reflections
5:26
Polarizing Sunglasses Have Vertical Polarizing Filters
5:48
Liquid Crystal Displays
6:08
LCDs Use Liquid Crystals in a Suspension That Align Themselves in a Specific Orientation When a Voltage is Applied
6:13
Cross-Orienting a Polarizer and a Matrix of Liquid Crystals so Light Can Be Modulated Pixel-by-Pixel
6:26
Example 1: Color of Light
7:30
Example 2: Analyzing an EM Wave
8:49
Example 3: Remote Control
9:45
Example 4: Comparing EM Waves
10:32
Reflection & Mirrors

24m 32s

Intro
0:00
Objectives
0:10
Waves at Boundaries
0:37
Reflected
0:43
Transmitted
0:45
Absorbed
0:48
Law of Reflection
0:58
The Angle of Incidence is Equal to the Angle of Reflection
1:00
They Are Both Measured From a Line Perpendicular, or Normal, to the Reflecting Surface
1:22
Types of Reflection
1:54
Diffuse Reflection
1:57
Specular Reflection
2:08
Example 1: Specular Reflection
2:24
Mirrors
3:20
Light Rays From the Object Reach the Plane Mirror and Are Reflected to the Observer
3:27
Virtual Image
3:33
Magnitude of Image Distance
4:05
Plane Mirror Ray Tracing
4:15
Object Distance
4:26
Image Distance
4:43
Magnification of Image
7:03
Example 2: Plane Mirror Images
7:28
Example 3: Image in a Plane Mirror
7:51
Spherical Mirrors
8:10
Inner Surface of a Spherical Mirror
8:19
Outer Surface of a Spherical Mirror
8:30
Focal Point of a Spherical Mirror
8:40
Converging
8:51
Diverging
9:00
Concave (Converging) Spherical Mirrors
9:09
Light Rays Coming Into a Mirror Parallel to the Principal Axis
9:14
Light Rays Passing Through the Center of Curvature
10:17
Light Rays From the Object Passing Directly Through the Focal Point
10:52
Mirror Equation (Lens Equation)
12:06
Object and Image Distances Are Positive on the Reflecting Side of the Mirror
12:13
Formula
12:19
Concave Mirror with Object Inside f
12:39
Example 4: Concave Spherical Mirror
14:21
Example 5: Image From a Concave Mirror
14:51
Convex (Diverging) Spherical Mirrors
16:29
Light Rays Coming Into a Mirror Parallel to the Principal Axis
16:37
Light Rays Striking the Center of the Mirror
16:50
Light Rays Never Converge on the Reflective Side of a Convex Mirror
16:54
Convex Mirror Ray Tracing
17:07
Example 6: Diverging Rays
19:12
Example 7: Focal Length
19:28
Example 8: Reflected Sonar Wave
19:53
Example 9: Plane Mirror Image Distance
20:20
Example 10: Image From a Concave Mirror
21:23
Example 11: Converging Mirror Image Distance
23:09
Refraction & Lenses

39m 42s

Intro
0:00
Objectives
0:09
Refraction
0:42
When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium
0:43
Wavelength Must Change If the Wave's Speed Changes
0:57
Refraction is When This Causes The Wave to Bend as It Enters the New Medium
1:12
Marching Band Analogy
1:22
Index of Refraction
2:37
Measure of How Much Light Slows Down in a Material
2:40
Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction
3:03
Indices of Refraction
3:21
Dispersion
4:01
White Light is Refracted Twice in Prism
4:23
Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency
4:41
Example 1: Determining n
5:14
Example 2: Light in Diamond and Crown Glass
5:55
Snell's Law
6:24
The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction
6:32
Light Bends Toward the Normal as it Enters a Material With a Higher n
7:08
Light Bends Toward the Normal as it Enters a Material With a Lower n
7:14
Example 3: Angle of Refraction
7:42
Example 4: Changes with Refraction
9:31
Total Internal Reflection
10:10
When the Angle of Refraction Reaches 90 Degrees
10:23
Critical Angle
10:34
Total Internal Reflection
10:51
Applications of TIR
12:13
Example 5: Critical Angle of Water
13:17
Thin Lenses
14:15
Convex Lenses
14:22
Concave Lenses
14:31
Convex Lenses
15:24
Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens
15:28
A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent
15:53
Example 6: Converging Lens Image
16:46
Example 7: Image Distance of Convex Lens
17:18
Concave Lenses
18:21
Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens
18:25
Concave Lenses Produce Upright, Virtual, Reduced Images
20:30
Example 8: Light Ray Thought a Lens
20:36
Systems of Optical Elements
21:05
Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element
21:16
Example 9: Lens and Mirrors
21:35
Thin Film Interference
27:22
When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film
27:25
If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere
27:31
Phase Change for Every Reflection from Low-Index to High-Index
28:09
Example 10: Thin Film Interference
28:41
Example 11: Wavelength in Diamond
32:07
Example 12: Light Incident on Crown Glass
33:57
Example 13: Real Image from Convex Lens
34:44
Example 14: Diverging Lens
35:45
Example 15: Creating Enlarged, Real Images
36:22
Example 16: Image from a Converging Lens
36:48
Example 17: Converging Lens System
37:50
Wave-Particle Duality

23m 47s

Intro
0:00
Objectives
0:11
Duality of Light
0:37
Photons
0:47
Dual Nature
0:53
Wave Evidence
1:00
Particle Evidence
1:10
Blackbody Radiation & the UV Catastrophe
1:20
Very Hot Objects Emitted Radiation in a Specific Spectrum of Frequencies and Intensities
1:25
Color Objects Emitted More Intensity at Higher Wavelengths
1:45
Quantization of Emitted Radiation
1:56
Photoelectric Effect
2:38
EM Radiation Striking a Piece of Metal May Emit Electrons
2:41
Not All EM Radiation Created Photoelectrons
2:49
Photons of Light
3:23
Photon Has Zero Mass, Zero Charge
3:32
Energy of a Photon is Quantized
3:36
Energy of a Photon is Related to its Frequency
3:41
Creation of Photoelectrons
4:17
Electrons in Metals Were Held in 'Energy Walls'
4:20
Work Function
4:32
Cutoff Frequency
4:54
Kinetic Energy of Photoelectrons
5:14
Electron in a Metal Absorbs a Photon with Energy Greater Than the Metal's Work Function
5:16
Electron is Emitted as a Photoelectron
5:24
Any Absorbed Energy Beyond That Required to Free the Electron is the KE of the Photoelectron
5:28
Photoelectric Effect in a Circuit
6:37
Compton Effect
8:28
Less of Energy and Momentum
8:49
Lost by X-Ray Equals Energy and Gained by Photoelectron
8:52
Compton Wavelength
9:09
Major Conclusions
9:36
De Broglie Wavelength
10:44
Smaller the Particle, the More Apparent the Wave Properties
11:03
Wavelength of a Moving Particle is Known as Its de Broglie Wavelength
11:07
Davisson-Germer Experiment
11:29
Verifies Wave Nature of Moving Particles
11:30
Shoot Electrons at Double Slit
11:34
Example 1
11:46
Example 2
13:07
Example 3
13:48
Example 4A
15:33
Example 4B
18:47
Example 5: Wave Nature of Light
19:54
Example 6: Moving Electrons
20:43
Example 7: Wavelength of an Electron
21:11
Example 8: Wrecking Ball
22:50
Section 7: Modern Physics
Atomic Energy Levels

14m 21s

Intro
0:00
Objectives
0:09
Rutherford's Gold Foil Experiment
0:35
Most of the Particles Go Through Undeflected
1:12
Some Alpha Particles Are Deflected Large Amounts
1:15
Atoms Have a Small, Massive, Positive Nucleus
1:20
Electrons Orbit the Nucleus
1:23
Most of the Atom is Empty Space
1:26
Problems with Rutherford's Model
1:31
Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons
1:39
Lose Energy When They Release Photons
1:46
Orbits Should Decay and They Should Be Unstable
1:50
Bohr Model of the Atom
2:09
Electrons Don't Lose Energy as They Accelerate
2:20
Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level
2:35
Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels
2:40
Energy Level Diagrams
3:29
n=1 is the Lowest Energy State
3:34
Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom
4:03
When Electron Reaches 0 eV It Is No Longer Bound
4:20
Electron Cloud Model (Probability Model)
4:46
Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus
4:53
Electron Orbitals Are Probability Regions
4:58
Atomic Spectra
5:16
Atoms Can Only Emit Certain Frequencies of Photons
5:19
Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels
5:34
This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element
5:37
Incandescence Emits a Continuous Energy
5:43
If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels
6:16
Continuous Spectrum
6:42
Absorption Spectrum
6:50
Emission Spectrum
7:08
X-Rays
7:36
The Photoelectric Effect in Reverse
7:38
Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate
7:53
Example 1: Electron in Hydrogen Atom
8:24
Example 2: EM Emission in Hydrogen
10:05
Example 3: Photon Frequencies
11:30
Example 4: Bright-Line Spectrum
12:24
Example 5: Gas Analysis
13:08
Nuclear Physics

15m 47s

Intro
0:00
Objectives
0:08
The Nucleus
0:33
Protons Have a Charge or +1 e
0:39
Neutrons Are Neutral (0 Charge)
0:42
Held Together by the Strong Nuclear Force
0:43
Example 1: Deconstructing an Atom
1:20
Mass-Energy Equivalence
2:06
Mass is a Measure of How Much Energy an Object Contains
2:16
Universal Conservation of Laws
2:31
Nuclear Binding Energy
2:53
A Strong Nuclear Force Holds Nucleons Together
3:04
Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus
3:19
Binding Energy of the Nucleus
3:32
Mass Defect
3:37
Nuclear Decay
4:30
Alpha Decay
4:42
Beta Decay
5:09
Gamma Decay
5:46
Fission
6:40
The Splitting of a Nucleus Into Two or More Nuclei
6:42
For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split
6:47
Fusion
8:14
The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus
8:15
This Fuels Our Sun and Stars
8:28
Basis of Hydrogen Bomb
8:31
Forces in the Universe
9:00
Strong Nuclear Force
9:06
Electromagnetic Force
9:13
Weak Nuclear Force
9:22
Gravitational Force
9:27
Example 2: Deuterium Nucleus
9:39
Example 3: Particle Accelerator
10:24
Example 4: Tritium Formation
12:03
Example 5: Beta Decay
13:02
Example 6: Gamma Decay
14:15
Example 7: Annihilation
14:39
Section 8: Sample AP Exams
AP Practice Exam: Multiple Choice, Part 1

38m 1s

Intro
0:00
Problem 1
1:33
Problem 2
1:57
Problem 3
2:50
Problem 4
3:46
Problem 5
4:13
Problem 6
4:41
Problem 7
6:12
Problem 8
6:49
Problem 9
7:49
Problem 10
9:31
Problem 11
10:08
Problem 12
11:03
Problem 13
11:30
Problem 14
12:28
Problem 15
14:04
Problem 16
15:05
Problem 17
15:55
Problem 18
17:06
Problem 19
18:43
Problem 20
19:58
Problem 21
22:03
Problem 22
22:49
Problem 23
23:28
Problem 24
24:04
Problem 25
25:07
Problem 26
26:46
Problem 27
28:03
Problem 28
28:49
Problem 29
30:20
Problem 30
31:10
Problem 31
33:03
Problem 32
33:46
Problem 33
34:47
Problem 34
36:07
Problem 35
36:44
AP Practice Exam: Multiple Choice, Part 2

37m 49s

Intro
0:00
Problem 36
0:18
Problem 37
0:42
Problem 38
2:13
Problem 39
4:10
Problem 40
4:47
Problem 41
5:52
Problem 42
7:22
Problem 43
8:16
Problem 44
9:11
Problem 45
9:42
Problem 46
10:56
Problem 47
12:03
Problem 48
13:58
Problem 49
14:49
Problem 50
15:36
Problem 51
15:51
Problem 52
17:18
Problem 53
17:59
Problem 54
19:10
Problem 55
21:27
Problem 56
22:40
Problem 57
23:19
Problem 58
23:50
Problem 59
25:35
Problem 60
26:45
Problem 61
27:57
Problem 62
28:32
Problem 63
29:52
Problem 64
30:27
Problem 65
31:27
Problem 66
32:22
Problem 67
33:18
Problem 68
35:21
Problem 69
36:27
Problem 70
36:46
AP Practice Exam: Free Response, Part 1

16m 53s

Intro
0:00
Question 1
0:23
Question 2
8:55
AP Practice Exam: Free Response, Part 2

9m 20s

Intro
0:00
Question 3
0:14
Question 4
4:34
AP Practice Exam: Free Response, Part 3

18m 12s

Intro
0:00
Question 5
0:15
Question 6
3:29
Question 7
6:18
Question 8
12:53
Section 9: Additional Examples
Metric Estimation

3m 53s

Intro
0:00
Question 1
0:38
Question 2
0:51
Question 3
1:09
Question 4
1:24
Question 5
1:49
Question 6
2:11
Question 7
2:27
Question 8
2:49
Question 9
3:03
Question 10
3:23
Defining Motion

7m 6s

Intro
0:00
Question 1
0:13
Question 2
0:50
Question 3
1:56
Question 4
2:24
Question 5
3:32
Question 6
4:01
Question 7
5:36
Question 8
6:36
Motion Graphs

6m 48s

Intro
0:00
Question 1
0:13
Question 2
2:01
Question 3
3:06
Question 4
3:41
Question 5
4:30
Question 6
5:52
Horizontal Kinematics

8m 16s

Intro
0:00
Question 1
0:19
Question 2
2:19
Question 3
3:16
Question 4
4:36
Question 5
6:43
Free Fall

7m 56s

Intro
0:00
Question 1-4
0:12
Question 5
2:36
Question 6
3:11
Question 7
4:44
Question 8
6:16
Projectile Motion

4m 17s

Intro
0:00
Question 1
0:13
Question 2
0:45
Question 3
1:25
Question 4
2:00
Question 5
2:32
Question 6
3:38
Newton's 1st Law

4m 34s

Intro
0:00
Question 1
0:15
Question 2
1:02
Question 3
1:50
Question 4
2:04
Question 5
2:26
Question 6
2:54
Question 7
3:11
Question 8
3:29
Question 9
3:47
Question 10
4:02
Newton's 2nd Law

5m 40s

Intro
0:00
Question 1
0:16
Question 2
0:55
Question 3
1:50
Question 4
2:40
Question 5
3:33
Question 6
3:56
Question 7
4:29
Newton's 3rd Law

3m 44s

Intro
0:00
Question 1
0:17
Question 2
0:44
Question 3
1:14
Question 4
1:51
Question 5
2:11
Question 6
2:29
Question 7
2:53
Friction

6m 37s

Intro
0:00
Question 1
0:13
Question 2
0:47
Question 3
1:25
Question 4
2:26
Question 5
3:43
Question 6
4:41
Question 7
5:13
Question 8
5:50
Ramps and Inclines

6m 13s

Intro
0:00
Question 1
0:18
Question 2
1:01
Question 3
2:50
Question 4
3:11
Question 5
5:08
Circular Motion

5m 17s

Intro
0:00
Question 1
0:21
Question 2
1:01
Question 3
1:50
Question 4
2:33
Question 5
3:10
Question 6
3:31
Question 7
3:56
Question 8
4:33
Gravity

6m 33s

Intro
0:00
Question 1
0:19
Question 2
1:05
Question 3
2:09
Question 4
2:53
Question 5
3:17
Question 6
4:00
Question 7
4:41
Question 8
5:20
Momentum & Impulse

9m 29s

Intro
0:00
Question 1
0:19
Question 2
2:17
Question 3
3:25
Question 4
3:56
Question 5
4:28
Question 6
5:04
Question 7
6:18
Question 8
6:57
Question 9
7:47
Conservation of Momentum

9m 33s

Intro
0:00
Question 1
0:15
Question 2
2:08
Question 3
4:03
Question 4
4:10
Question 5
6:08
Question 6
6:55
Question 7
8:26
Work & Power

6m 2s

Intro
0:00
Question 1
0:13
Question 2
0:29
Question 3
0:55
Question 4
1:36
Question 5
2:18
Question 6
3:22
Question 7
4:01
Question 8
4:18
Question 9
4:49
Springs

7m 59s

Intro
0:00
Question 1
0:13
Question 4
2:26
Question 5
3:37
Question 6
4:39
Question 7
5:28
Question 8
5:51
Energy & Energy Conservation

8m 47s

Intro
0:00
Question 1
0:18
Question 2
1:27
Question 3
1:44
Question 4
2:33
Question 5
2:44
Question 6
3:33
Question 7
4:41
Question 8
5:19
Question 9
5:37
Question 10
7:12
Question 11
7:40
Electric Charge

7m 6s

Intro
0:00
Question 1
0:10
Question 2
1:03
Question 3
1:32
Question 4
2:12
Question 5
3:01
Question 6
3:49
Question 7
4:24
Question 8
4:50
Question 9
5:32
Question 10
5:55
Question 11
6:26
Coulomb's Law

4m 13s

Intro
0:00
Question 1
0:14
Question 2
0:47
Question 3
1:25
Question 4
2:25
Question 5
3:01
Electric Fields & Forces

4m 11s

Intro
0:00
Question 1
0:19
Question 2
0:51
Question 3
1:30
Question 4
2:19
Question 5
3:12
Electric Potential

5m 12s

Intro
0:00
Question 1
0:14
Question 2
0:42
Question 3
1:08
Question 4
1:43
Question 5
2:22
Question 6
2:49
Question 7
3:14
Question 8
4:02
Electrical Current

6m 54s

Intro
0:00
Question 1
0:13
Question 2
0:42
Question 3
2:01
Question 4
3:02
Question 5
3:52
Question 6
4:15
Question 7
4:37
Question 8
4:59
Question 9
5:50
Resistance

5m 15s

Intro
0:00
Question 1
0:12
Question 2
0:53
Question 3
1:44
Question 4
2:31
Question 5
3:21
Question 6
4:06
Ohm's Law

4m 27s

Intro
0:00
Question 1
0:12
Question 2
0:33
Question 3
0:59
Question 4
1:32
Question 5
1:56
Question 6
2:50
Question 7
3:19
Question 8
3:50
Circuit Analysis

6m 36s

Intro
0:00
Question 1
0:12
Question 2
2:16
Question 3
2:33
Question 4
2:42
Question 5
3:18
Question 6
5:51
Question 7
6:00
Magnetism

3m 43s

Intro
0:00
Question 1
0:16
Question 2
0:31
Question 3
0:56
Question 4
1:19
Question 5
1:35
Question 6
2:36
Question 7
3:03
Wave Basics

4m 21s

Intro
0:00
Question 1
0:13
Question 2
0:36
Question 3
0:47
Question 4
1:13
Question 5
1:27
Question 6
1:39
Question 7
1:54
Question 8
2:22
Question 9
2:51
Question 10
3:32
Wave Characteristics

5m 33s

Intro
0:00
Question 1
0:23
Question 2
1:04
Question 3
2:01
Question 4
2:50
Question 5
3:12
Question 6
3:57
Question 7
4:16
Question 8
4:42
Question 9
4:56
Wave Behaviors

3m 52s

Intro
0:00
Question 1
0:13
Question 2
0:40
Question 3
1:04
Question 4
1:17
Question 5
1:39
Question 6
2:07
Question 7
2:41
Question 8
3:09
Reflection

3m 48s

Intro
0:00
Question 1
0:12
Question 2
0:50
Question 3
1:29
Question 4
1:46
Question 5
3:08
Refraction

2m 49s

Intro
0:00
Question 1
0:29
Question 5
1:03
Question 6
1:24
Question 7
2:01
Diffraction

2m 34s

Intro
0:00
Question 1
0:16
Question 2
0:31
Question 3
0:50
Question 4
1:05
Question 5
1:37
Question 6
2:04
Electromagnetic Spectrum

7m 6s

Intro
0:00
Question 1
0:24
Question 2
0:39
Question 3
1:05
Question 4
1:51
Question 5
2:03
Question 6
2:58
Question 7
3:14
Question 8
3:52
Question 9
4:30
Question 10
5:04
Question 11
6:01
Question 12
6:16
Wave-Particle Duality

5m 30s

Intro
0:00
Question 1
0:15
Question 2
0:34
Question 3
0:53
Question 4
1:54
Question 5
2:16
Question 6
2:27
Question 7
2:42
Question 8
2:59
Question 9
3:45
Question 10
4:13
Question 11
4:33
Energy Levels

8m 13s

Intro
0:00
Question 1
0:25
Question 2
1:18
Question 3
1:43
Question 4
2:08
Question 5
3:17
Question 6
3:54
Question 7
4:40
Question 8
5:15
Question 9
5:54
Question 10
6:41
Question 11
7:14
Mass-Energy Equivalence

8m 15s

Intro
0:00
Question 1
0:19
Question 2
1:02
Question 3
1:37
Question 4
2:17
Question 5
2:55
Question 6
3:32
Question 7
4:13
Question 8
5:04
Question 9
5:29
Question 10
5:58
Question 11
6:48
Question 12
7:39
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Lecture Comments (64)

1 answer

Last reply by: Professor Dan Fullerton
Tue Aug 10, 2021 6:48 AM

Post by Derek Chen on August 9, 2021

Hi Dan, how does the graph for example 11 look like how it is? Doesn't the velocity slow down faster and faster as it reaches the top? So it would be curved downward, going down faster and faster.

1 answer

Last reply by: Professor Dan Fullerton
Sun Jan 31, 2021 1:11 PM

Post by oli642107 on January 31, 2021

Hi Dan,

For example 9: d-t graph (at 22:24), why isn't the correct answer by graph (2), but graph (4)? Can you explain further, because I am having trouble understanding this part. Thank you!

0 answers

Post by Jl on July 8, 2019

Hi Dan,
On the acceleration graph, why is the acceleration positive, then it becomes negative? Since it is accelerating towards the ground, and the velocity is negative, then positive, shouldn't the acceleration be negative, then positive?

1 answer

Last reply by: Professor Dan Fullerton
Wed Jun 26, 2019 2:03 PM

Post by Shahd Al-mur on June 25, 2019

Hello Dan, Can you please help me out with solving this question:
A squirrel completing short glide travel in a straight line tipped 40 (degrees)below the horizontal. the squirrel starts 9.0m above the ground on one tree. and glides to a second tree that is a horizontal distance 3.5m way:
a) what is the length of the squirrel's glide.
b) what is the squirrel's hight above the ground when it lands?

1 answer

Last reply by: Professor Dan Fullerton
Mon Jun 6, 2016 9:36 PM

Post by Summer Breeze on June 6, 2016

Hello Dan, Why doesn't a block accelerating an incline graph look like graph 2. I don't see how it is graph 4.

1 answer

Last reply by: Professor Dan Fullerton
Mon Jun 6, 2016 9:37 PM

Post by Summer Breeze on June 6, 2016

Hello Dan, Looking at the Velocity/graph, how can you tell from 5seconds to 10 seconds that we are still at 5m position? You mentioned it but I dont see it. If the latter is true, then what about at 4secs. We know from the P/T graph, that at 4 seconds we are not at 5m position, but the V/T graph suggests otherwise because 4sec falls inside the area of the 5m rectangle

0 answers

Post by Summer Breeze on June 6, 2016

Hello Dan, Can you please tell me when in the Velocity /Time graph explanation does it become obvious that our position is 0? I can see it in the position /time graph, but I cant see it in the velocity/time graph.

2 answers

Last reply by: Summer Breeze
Mon Jun 6, 2016 3:11 PM

Post by Summer Breeze on June 4, 2016

Hello Dan, In section where you ask the total distance travelled by looking at the trapezeshape; you calculate the area of the triangle and rectangle, but my image of total distance traveled is the perimeter of a shape and not its area. Could you please tell me the intuition behing looking for the total distance traveled by calcuting the area?

1 answer

Last reply by: Ann Gao
Mon Aug 17, 2020 9:14 AM

Post by Summer Breeze on June 4, 2016

Hello Dan, for the dog example of -2m/s. You say that the 'negative' indicates the direction. How does a dog moving in a negative direction look like? I think if I can visualize it, then a negative direction would be more intuitive for me.

2 answers

Last reply by: Professor Dan Fullerton
Tue Jul 9, 2019 11:24 AM

Post by Summer Breeze on June 4, 2016

Hello Dan, relative acceleration, I can't understand why there would be negative direction. What does it mean to have negative direction?

0 answers

Post by Summer Breeze on June 4, 2016

Hello Dan, I have never understood the concept of a car moving to the left/negative velocity and accelerating to the left. This seems so counterintuive. For me a car moves forward and increases in velocity in doing so; acceleration happens forward to me. How can a car move to the left and increase speed and velocity to the left?

0 answers

Post by Summer Breeze on June 4, 2016

Hello Dan, you mentioned that instantaneous velocity is different from average velocity. Can you please define instantaneous velocity?

5 answers

Last reply by: Professor Dan Fullerton
Mon Jun 6, 2016 5:13 PM

Post by Summer Breeze on June 4, 2016

Hello Dan, Can you please show me in simple Math how 3m/s/s is = 3m/s to the second power (sorry, my PC is acting, so I can't use the symbol to the second power)?

1 answer

Last reply by: Professor Dan Fullerton
Mon Oct 12, 2015 1:11 PM

Post by Jim Tang on October 10, 2015

hey,

at 11:44, how come the maximum instantaneous velocity is calculated over a time interval? i thought it was at a specific point.

1 answer

Last reply by: Professor Dan Fullerton
Thu Mar 19, 2015 6:26 AM

Post by Rasheed Abdullah on March 18, 2015

Hey Mr. Fullerton

Thanks for the great lecture. Do you know where I could find some practice problems that go over this section of physics?

Thank You,

Rasheed

2 answers

Last reply by: Jingyi Feng
Sun Dec 21, 2014 4:57 PM

Post by Jingyi Feng on December 19, 2014

Hello Mr.Fullerton,
I did not understand the graph about acceleration in the example 10. Why the acceleration became positive when the ball touched the ground? Acceleration should not always be -9.8m/s^2 in this case?

thank you!!

2 answers

Last reply by: MOGIN Daniloff
Fri Nov 28, 2014 6:59 PM

Post by MOGIN Daniloff on November 26, 2014

Hi,
In example 10 the position function of the first graph has a constant negative slope going to 0 and a constant positive slope going back up. This cannot be true given that the velocity graph is not constant. Therefore, the first graph is inaccurate. Or am I missing something?

1 answer

Last reply by: Professor Dan Fullerton
Mon Oct 20, 2014 3:36 PM

Post by alina trandafir on October 20, 2014


If you are asked to rank velocity from greatest to smallest how do you look at negatives?

10 m/s north; 0; -15m/s north vs
10 m/s north; -15m/s north; 0

If average speed?
-15m/s north; 10 m/s north; 0;

Please help. Thank!
Sorry for so many posts.

1 answer

Last reply by: Professor Dan Fullerton
Mon Oct 20, 2014 3:35 PM

Post by alina trandafir on October 20, 2014

Sorry I forgot to include this but simply positive and negative could be a direction correct?  So how do you tell the difference between a scalar and vector with same units?

1 answer

Last reply by: Professor Dan Fullerton
Mon Oct 20, 2014 3:35 PM

Post by alina trandafir on October 20, 2014

Hi,
Quick question.  Basically I am trying to understand can you have a scalar with multidimensional units but it must not have a direction attached to it to be a scalar?

Say 10newtons or 10 kgâ‹…m/s2 which is in contrast to 10 newtons upwards?
10newtons upward is a vector but simply 10newtons is a scalar correct??

Please Help.  Thank you!!

1 answer

Last reply by: Professor Dan Fullerton
Wed Sep 17, 2014 4:09 PM

Post by Martin Zheng on September 17, 2014

Hello Professor Fullerton,

The middle graph of example 8 shows that the velocity of the ball was negative and turned to positive. However, the ball is always under Bobbi's hand, so isn't the velocity suppose to stay negative?

Sincerely
Martin

1 answer

Last reply by: Professor Dan Fullerton
Wed Sep 11, 2013 1:26 PM

Post by Andrei Afilipoaei on September 11, 2013

Hello Mr. Fullerton

At the example 6 with the acceleration of Monty the Monkey:
we know acceleration is a vector; shouldn't it have a direction when we calculate acceleration?

Thank you

Andrei

3 answers

Last reply by: Professor Dan Fullerton
Sun Oct 20, 2013 5:52 PM

Post by Gaurav Kumar on September 9, 2013

Would a graph of position versus time squared be equivalent to a velocity vs time graph?

4 answers

Last reply by: Larry wang
Thu Aug 22, 2013 2:36 PM

Post by Larry wang on August 22, 2013

On Example 12; the entire journey I think was broken up in two parts. Since y=0 the origin: Falling down (-ve Y) and Bouncing back up (+ve Y), correct. From the a-t graph g was constant and negative throughout the entire journey, except during the spike when it's velocity changes . Can't we simply first draw g to be positive and when the ball rises up to be negative.
Is it because we are taking account (-ve Y axis) therefore sign wise it's  -g and when the ball rises +ve Y (still -g) since against the gravity. Is this explanation correct.    

1 answer

Last reply by: Professor Dan Fullerton
Sat May 4, 2013 7:53 AM

Post by Jane Lee on May 3, 2013

I am just as confused as Norma is on Example 8. Could you please explain?

4 answers

Last reply by: Professor Dan Fullerton
Sun Oct 20, 2013 5:53 PM

Post by Norma Saderi Moreira on April 8, 2013

Hello Professor Fullerton,
the example 8 is asked to find the distance and not the displacement and then it was calculated the area of the graph. In this last example you said displacement and then calculated area of graph. I'm little confused . Would you mind give some more thoughts about that ?

Related Articles:

Defining & Graphing Motion

  • Motion can be described by position, displacement, distance, velocity, speed, and acceleration.
  • The linear motion of a system can be described by the displacement, velocity, and acceleration of its center of mass.
  • Acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time.
  • The slope of the x-t graph gives you velocity.
  • The slope of the v-t graph gives you acceleration, and the area under the v-t graph gives you the change in displacement.
  • The area under the a-t graph gives you the change in velocity.

Defining & Graphing Motion

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  1. Intro
    • Objectives
      • Position
      • Distance
      • Example 1: Distance
        • Displacement
        • Example 2: Displacement
          • Average Speed
          • Example 3: Average Speed
            • Average Velocity
            • Example 4: Average Velocity
              • Example 5: Chuck the Hungry Squirrel
                • Acceleration
                • Example 6: Acceleration Problem
                  • Average vs. Instantaneous
                  • Example 7: Average Velocity
                    • Particle Diagrams
                    • Position-Time Graphs
                    • Slope of x-t Graph
                    • Velocity-Time Graphs
                    • Area Under v-t Graphs
                    • Example 8: Slope of a v-t Graph
                      • Acceleration-Time Graphs
                      • Example 10: Motion Graphing
                        • Example 11: v-t Graph
                          • Example 12: Displacement From v-t Graph
                            • Intro 0:00
                            • Objectives 0:07
                            • Position 0:40
                              • An Object's Position Cab Be Assigned to a Variable on a Number Scale
                              • Symbol for Position
                            • Distance 1:13
                              • When Position Changes, An Object Has Traveled Some Distance
                              • Distance is Scalar and Measured in Meters
                            • Example 1: Distance 1:34
                            • Displacement 2:17
                              • Displacement is a Vector Which Describes the Straight Line From Start to End Point
                              • Measured in Meters
                            • Example 2: Displacement 2:39
                            • Average Speed 3:32
                              • The Distance Traveled Divided by the Time Interval
                              • Speed is a Scalar
                            • Example 3: Average Speed 3:57
                            • Average Velocity 4:37
                              • The Displacement Divided by the Time Interval
                              • Velocity is a Vector
                            • Example 4: Average Velocity 5:06
                            • Example 5: Chuck the Hungry Squirrel 5:55
                            • Acceleration 8:02
                              • Rate At Which Velocity Changes
                              • Acceleration is a Vector
                            • Example 6: Acceleration Problem 8:52
                            • Average vs. Instantaneous 9:44
                              • Average Values Take Into Account an Entire Time Interval
                              • Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time
                            • Example 7: Average Velocity 10:06
                            • Particle Diagrams 11:57
                              • Similar to the Effect of Oil Leak from a Car on the Pavement
                              • Accelerating
                            • Position-Time Graphs 14:17
                              • Shows Position as a Function of Time
                            • Slope of x-t Graph 15:08
                              • Slope Gives You the Velocity
                              • Negative Indicates Direction
                            • Velocity-Time Graphs 16:45
                              • Shows Velocity as a Function of Time
                            • Area Under v-t Graphs 17:47
                              • Area Under the V-T Graph Gives You Change in Displacement
                            • Example 8: Slope of a v-t Graph 19:45
                            • Acceleration-Time Graphs 21:44
                              • Slope of the v-t Graph Gives You Acceleration
                              • Area Under the a-t Graph Gives You an Object's Change in Velocity
                            • Example 10: Motion Graphing 24:03
                            • Example 11: v-t Graph 27:14
                            • Example 12: Displacement From v-t Graph 28:14

                            Transcription: Defining & Graphing Motion

                            Hi everyone and welcome back to Educator.com.0000

                            Today I want to talk about defining and graphing motion.0003

                            Our objectives are going to be to understand the difference between position, distance, and displacement.0007

                            Our second objective is to understand the difference between speed and velocity.0013

                            Our third objective is to solve problems involving average speed and velocity and calculating distance displacement, speed velocity, and acceleration.0016

                            Our fourth objective will be constructing and interpreting graphs and diagrams of position, velocity, and acceleration versus time.0024

                            And finally, we will be determining and interpreting slopes and areas of motion graphs in order to help us understand what these quantities are.0030

                            So, with that, let us dive right in. Let us first define position.0039

                            An object’s position in a one-dimension -- you can assign it to a variable on a number scale.0043

                            Very simply, if we make this an x-axis, for example, we can put an object’s position anywhere on that x-axis and it describes where that is at a specific point in time.0048

                            Ha! There it is. You can assign whatever you want to be the 0-point as well as the positive and negative directions.0060

                            Now the symbol for positioning in one-dimension is x.0067

                            If we look at distance when position changes, an object has traveled some amount of distance.0071

                            The more position changes, the more distance is traveled.0077

                            Distance is a scalar. It has a magnitude only -- no direction.0080

                            And its standard measurement is in meters (m). Distance is a scalar -- no direction.0086

                            So let us take a look at an example here.0095

                            We have a deer that walks 1300 m East to a creek for a drink.0097

                            The deer then walks 500 m West to the berry patch for dinner.0100

                            Then it runs 300 m West when startled by a loud, fierce raccoon.0104

                            What total distance did the deer travel? Well, in order to do this, let us just take a look.0108

                            The deer traveled 1300 m East, then 500 m West, and then 300 m West.0114

                            So the total distance traveled, 1300 + 500 + 300, should be right around 2100 m.0123

                            Very straightforward. No direction required.0132

                            Displacement, on the other hand, is a vector which describes the straight line distance from where you start to where you end.0137

                            It includes a direction. It is a vector.0144

                            Displacement, final x position minus initial x position or we also call that Δ (delta) x is also measured in meters.0147

                            So let us take a look at an example now with displacement.0157

                            Same basic story, slightly different take on it.0161

                            Now our deer walks 1300 m East to the creek, then walks 500 m West to the berry patch, and then runs 300 m West when startled by a loud raccoon.0164

                            What is the deer's displacement? Well to find the displacement, we go from a starting point to our final point.0180

                            He went 1300 m East and then 500 West and 300 West.0187

                            Well, the total from the starting point to its final point, must be 500 m East.0192

                            So the deer's displacement, 500 m East.0200

                            Displacement is a vector, therefore, it must have a direction as well.0206

                            Now average speed tells you the distance traveled divided by the total time it took to travel that.0212

                            And we give it the symbol v with a line over it. The line over it meaning average.0218

                            So that is the distance traveled divided by the time.0223

                            Speed is a scalar -- S-S and its measured in meters per second (m/s).0226

                            So let us take our same example and let us look at average speed.0233

                            The deer walked 1300 m East, then 500 m West, and then ran 300 m West.0237

                            It did that entire trip in 600 seconds (s).0242

                            If that is the case, to find the average speed for the entire trip, v-average, average speed equals total distance traveled divided by the time it took.0246

                            We already found the total distance traveled is 2100 m and the time it took, 600 s.0257

                            Just a little bit of math and I find out that the average speed was 3.5 m/s.0266

                            Moving on, average velocity is the displacement divided by the time interval.0276

                            Since it is a displacement and displacement is a vector, average velocity is also a vector.0282

                            It is also measured in m/s, but it includes a direction.0288

                            Average velocity, again same symbol, v with a line over it, so we have got to be careful.0292

                            It is x - x initial over the time it took or Δx/T.0298

                            Let us look at that in the context of our same example as well.0304

                            Deer walked 1300 m East to the creek, 500 West for dinner, and then ran 300 m West.0307

                            What is the average velocity, the vector, if the entire trip took 600 s?0313

                            Once again, we are going to start off with the same sort of math.0319

                            The average is going to be equal to the displacement divided by the time.0323

                            But now our displacement is 500 m East. The time it took was 600 s.0328

                            500/600 is going to be 0.833 m/s and since it is a velocity -- it is a vector -- it must have a direction to go along with it.0335

                            Let us see if we cannot put all of that together.0352

                            Here is our problem with our dear friend, Chuck, the hungry squirrel.0355

                            Chuck, the hungry squirrel, travels 4 m East and 3 m North in search of an acorn.0358

                            The entire trip takes him 20 s. Find the distance he travels, his displacement, his average speed, and his average velocity.0364

                            Well distance traveled, if he went 4 m East and 3 m North, how far did he go?0374

                            He went 7 m -- distance --7 m.0381

                            What is his displacement? Well to do that we need to figure out how far he went from his starting point to his ending point.0383

                            He started off down here. He went 4 m East, then he went 3 m North.0389

                            His displacement then, is going to be the vector from the starting point of the first to the ending point of our last.0400

                            There is our displacement. That is a 3/4 5 triangle or you could find the magnitude of that by the Pythagorean Theorem.0406

                            You should still come up with 5 m. So his displacement, Δx must be 5 m and direction -- he went Northeast.0414

                            How about his average speed? Again, average speed is going to be distance divided by time.0425

                            His distance we just found was 7 m. It took 20 s, so that is going to be 0.35 m/s for his average speed.0433

                            Average velocity, on the other hand, is going to be his displacement divided by time.0447

                            Displacement was 5 m to the Northeast in 20 s or 0.25 m/s Northeast.0453

                            It has a direction, it is a velocity.0464

                            So note very carefully here, average speed and average velocity do not have to have the exact same numerical value, even when you are talking about very similar paths or the same paths.0467

                            All right -- acceleration. Acceleration is the rate at which velocity changes.0480

                            If everybody just kept going a constant velocity, the same speed, it would be a pretty boring world.0487

                            So when velocity changes, we call it an acceleration. It is the change in velocity divided by the time.0492

                            And Δv or Δanything is always the final value minus the initial value.0498

                            Acceleration, too, is a vector. It has a direction and its units are meters per second per second.0504

                            What that means is if your speed changes -- if your acceleration is 5 m/s/s, your speed increases by 5 m/s every second.0511

                            I should say your velocity changes 5 m/s, every second.0520

                            We also call that a meter per second squared (m/s 2).0525

                            All right. Let us take a look at an example with acceleration.0529

                            Monte, the monkey, accelerates from rest, so his initial velocity is 0, to a velocity of 9 m/s.0534

                            V = 9 m/s in a time span of 3 s. Find Monte's acceleration.0543

                            Now acceleration is change in velocity divided by time or final velocity minus initial velocity divided by time.0548

                            That is going to be 9 m/s - 0/3 s or 3 m/s/s, which we would typically write as 3 m/s 2.0559

                            Very straightforward. A simple problem in acceleration, but hopefully it starts giving you the idea.0577

                            Now, we have to talk a little bit about average values versus instantaneous values. They are not the same thing.0582

                            Average values take into account an entire time interval.0591

                            Instantaneous time values tell you the rate of change of a quantity at a specific instant in time at that specific point.0594

                            They are not always the same. So let us take a look at a problem with average velocity.0602

                            A motorcyclist travels 30 km in 20 minutes. 30 km in 20 minutes -- there is part of our trip -- at a constant velocity.0610

                            He takes a 10 minute break, then travels 30 km in 30 minutes at a constant velocity.0617

                            Find the cyclist's minimum instantaneous velocity, maximum instantaneous velocity, and average velocity.0626

                            It is pretty easy to see the minimum instantaneous velocity is going to occur here where they are taking a break.0634

                            Position is not changing -- velocity is 0. So the minimum instantaneous velocity is 0.0640

                            Where are we going to have the maximum instantaneous velocity?0648

                            Well, that is going to be when we travel the biggest distance in the smallest amount of time, or up here we are traveling 30 km in 20 minutes.0651

                            So the max is going to be 30 km/20 minutes or 1.5 km/min.0660

                            Now to find the average velocity though, we have to take into account the entire trip.0675

                            Average velocity is going to be the total displacement, 60 km, divided by the total time.0682

                            20 + 10 + 30 is 60 minutes, which will be 1 kilometer per minute (km/m).0691

                            And note here that the average velocity is between the minimum and maximum -- always going to be either between or equal to the minimum or maximum.0699

                            It cannot be outside that and be a real average velocity. A great check on your problem solving.0708

                            Let us take a look at particle diagrams.0715

                            It is kind of similar to the effect you might see if you had an old leaky car that has an oil leak and every second, every specific instance in time, it leaks one drop of oil.0718

                            It is a consistent drop every specified unit of time.0727

                            So if we were traveling down the road to the right in our car at a constant speed, we would see oil drops hit the ground evenly spaced.0732

                            Because they are evenly spaced, you know the car is moving at a constant velocity.0744

                            So just by looking at the oil drops you would be able to go take a look and see exactly what is happening.0746

                            Now when you looked at these, there are a couple of questions that might remain in your mind.0753

                            You are pretty certain the car is traveling at constant velocity, but can you tell if it is traveling to the right or to the left just from the oil drops.0757

                            Now assuming that you were not looking on which side of the road they were on, you really cannot tell.0765

                            But you do know that regardless, the acceleration is 0.0770

                            It is moving at constant velocity because these are all evenly spaced -- same spacing between each of the drops.0777

                            On the other hand, what if our car was accelerating to the right?0782

                            Our particle diagram is now non-uniformed. We have smaller spacings over here and bigger spacings over here.0786

                            Drops are getting further apart, velocity is changing, the car is accelerating.0795

                            Can you think of a case in which the car could have a negative velocity and a negative acceleration, yet speed up?0801

                            Think about it for a second.0810

                            Here is our car -- put some wheels on it and make it a nice, pretty little car. There it is.0811

                            If it has a velocity to the left and we have called to the left negative, that would be a negative velocity.0819

                            If it is accelerating in that direction, it is going faster and faster and the velocity to the left is getting bigger and bigger in magnitude, but that is a negative acceleration.0825

                            Negative acceleration does not mean slowing down. It is not decelerating.0836

                            Negative acceleration just means that you are accelerating in whatever direction you have called negative.0841

                            If you have velocity and acceleration in the same direction, the car will be speeding up.0847

                            Its speed will be increasing.0854

                            Let us take a look at some motion graphs.0858

                            One of the most popular types is a position time graph. It shows an objects position as a function of time.0861

                            So let us assume that we have some cute little dog that wanders away from our house at a constant 1 m/s.0866

                            So the dog does that -- starts at time 0 -- wanders away from the house for a little bit, so the position is getting further and further away from this origin -- the house -- until here the dog decides it has had enough and takes a five second rest.0872

                            It bops down in the grass in the backyard for 5 s. Its position does not change.0885

                            Then the dog returns to the house at 2 m/s.0890

                            So it is going back the opposite direction and we end up with a little bit steeper slope because it is coming back to the house faster.0894

                            There is a basic position time graph. We can learn an awful lot from this graph though.0902

                            The slope of this graph tells you the dogs velocity at any given point in time.0909

                            For the first part of the trip, if we take the slope of the graph -- right here -- the slope there is going to be rise over run.0913

                            We rise 1, 2, 3, 4, 5 meters in a time of 1, 2, 3, 4, 5 seconds or 1 m/s. That is the dog's velocity. Remember?0927

                            So the slope of a position time graph, gives you the velocity.0942

                            Let us take a look here when the dog's taking a rest.0947

                            Slope of a flat line is 0. The dog's velocity was 0.0950

                            Let us take a look here coming back to the house over here on the right.0954

                            The slope there again, rise over run. Our rise now is 1, 2, 3, 4, 5, but it is in the opposite direction.0959

                            It is going down, so our rise is -5 meters and the time it took goes from 10, 11, 12, 12 1/2 -- 2.5 seconds.0969

                            So I come up with a slope of -2 m/s.0979

                            The velocity of the dog is -2 m/s -- where that negative sign -- all that is telling you is that the negative is indicating the direction.0984

                            So position time graphs can be a very useful tool for describing the motion of an object.0998

                            We could also make a velocity time graph. It shows the velocity of an object as a function of time.1004

                            It is related to the position time graph by the slope.1012

                            So here is the position time graph we were just talking about for the dog wandering away from the house and back.1015

                            Down below we have the velocity time graph for basically the same information.1021

                            Initially, the dog's velocity, the slope here was 1 m/s, so our velocity down here for that same time interval of 5 s is 1 m/s.1027

                            Then the dog took a rest for a couple of seconds -- velocity was 0 -- slope was 0.1038

                            Here we have a value on our velocity time graph of 0 for that same time interval.1044

                            Now to end the story, the dog came back to the house -- our slope was -2 m/s.1051

                            Our velocity down here is -2 m/s for the same time interval, so these graphs are very closely related.1057

                            We can look at the area under the velocity time graph to tell us the change in the displacement of the dog even.1068

                            Here is how that works.1073

                            As we look at the area under the graph of our velocity time graph -- if we take this area, the velocity under the graph, the area between the 0 line and where our graph is, we get that rectangle.1075

                            The area of that rectangle is length times width.1089

                            Our length is 5 s. Our width is 1 m/s, which is 5 m.1094

                            By the time we get to 5, our area is 5 m, but a look at our position time graph, right at that point, the position is 5 m.1103

                            If we keep going through our graph and say "Hey over here at 8 s, what total area do we have?"1112

                            All the area to the left of that 8 s is still 5 m, so over here at 8 s, our position is still 5 m.1119

                            And if we keep going -- if we wanted to say what is the dog's position over here at 12 1/2 s -- well -- now we have another area to take into account.1128

                            We also have this rectangle and since it is below the line -- although in math they may tell you there is not officially a negative area, there is a meaning to negative areas on the graphs in physics -- that area, which is going to be length times width -- we have 2 1/2 s width and we have -2 m/s.1138

                            So 2 1/2 x -2 is going to be -5 m.1162

                            So all of the area added up to the left of this red line -- we have +5 and -5 gets us 0.1167

                            But look, down here at exactly that point in time. 12 1/2 s, just like we have here, our position is back to 0.1173

                            Now the slope of the VT graph, the velocity time graph, can also give you a lot of information.1186

                            It can give you the acceleration. So with a problem like this, we can also look and say, "What is the acceleration of the car at T = 5 s?1192

                            Well at T = 5 s -- what we have is a slope of 0.1203

                            So the acceleration at that point -- 0 m/s 2.1209

                            How about the total distance traveled by the car during the 6 s interval?1215

                            Well, to get the total distance traveled, we need to take the area under all of this.1220

                            How do you take the area of that? A couple of ways to do it, but probably the easiest in my mind is I would break this up into a couple of shapes.1230

                            Over here we have a triangle and on the right hand side we have a rectangle.1237

                            Let us add up their areas to find the total distance traveled.1243

                            Total distance traveled is going to be the area of our red triangle, 1/2 base times height, plus the area of our blue rectangle.1248

                            One-half our base is 4 s. Our height is 10 m/s and our rectangle -- our length is from 4-6 -- 2 s, and a height of 10 m/s.1261

                            So 1/2 x 4 x 10 -- that is going to be 20 m + 2 x 10 -- 20 m -- for my grand answer of 40 m traveled.1279

                            All right -- how we can use slopes and areas.1298

                            Now, acceleration time graphs -- you get by taking the slope of the velocity time graph.1304

                            So, if you take the area under the acceleration time graph, you get the objects change in velocity.1311

                            We have a pattern here. We started with position time graphs.1316

                            If we took the slope, we got velocity.1320

                            If we have a velocity time graph and we take the slope, we get acceleration -- or the other direction -- if we take the area under the acceleration time graph, we get the change in velocity.1322

                            From the velocity time graph, if we take the area, we get the change in position.1332

                            You can keep going with this pattern forward and backwards to find whatever information you need to based on these motion graphs.1336

                            Let us take a look at another example with a position times, sometimes distance time graph.1345

                            Which graph here best represents the motion of a block accelerating uniformly down an inclined plane?1350

                            Well let us think about what is going to happen if we have some inclined plane or a ramp and we have a block that is accelerating down the ramp.1358

                            Initially it is going to be at position 0 and over time it is going to get a larger and larger distance traveled.1369

                            So, right away, we can eliminate number one on our choices.1378

                            Now, as it goes faster and faster, it is going to cover more and more distance.1383

                            We would also think of that as seeing that. . . .1389

                            If we looked over here at a velocity time graph, we could make a velocity time graph and say "You know, it probably starts at some 0 velocity and goes faster and faster and faster."1392

                            Well if that is the case, we also need to look at something where the area is getting progressively bigger, therefore the distance traveled must be getting progressively greater for the same time interval.1403

                            The correct answer must be that one.1415

                            And we could also look at it from the opposite direction. Right here, the slope is 0, so we have a velocity of 0.1418

                            Here we have a bigger slope. We have a bigger velocity.1424

                            Here we have a very big slope. We have a very big velocity as time increases.1428

                            Therefore, that would be the graph that best represents the motion of a block accelerating uniformly down an inclined plane.1434

                            Let us take a look at a little bit of a challenging one. See if we cannot push a little bit.1444

                            Bobbie dribbles the basketball on the ground.1448

                            Draw the position time graph, the velocity time graph, and the acceleration time graph for the basketball as it travels down from Bobbie's hand -- bounces back up to her hand.1450

                            We will assume the floor is position Y = 0.1460

                            So let us start by making a graph of position Y versus time.1464

                            Let us make one for velocity versus time and let us make one for acceleration versus time.1472

                            All right. Initially the ball is going to start off in Bobbie's hand.1484

                            So position-wise, it is going to start up here at some positive value.1488

                            We also know after a little while, it is going to hit the ground -- position 0 -- and as it comes back up to Bobbie's hand, it is going to come back to where it started.1493

                            So we have those points for position.1500

                            Now for velocity, let us assume that Bobbie drops it as opposed to really pushing it, just to make it a little simpler.1505

                            That means its initial velocity is going to have to be 0.1510

                            As it is traveling down towards the ground, it is going to go faster and faster.1514

                            Then the moment it hits the ground, its velocity switches its direction, but keeps roughly the same magnitude.1519

                            So we are going to have to have this jump back up here and as it comes back up to Bobbie's hand, it gets slower and slower and slower until its velocity is 0 right at her hand level.1526

                            So we are going to have to have something like that and we will fill in some of the other points in a minute.1535

                            As far as acceleration goes, the entire time the objects in the air and nothing's touching it, it is acceleration is the acceleration due to gravity here on Earth.1541

                            It is constant. It does not change.1550

                            It is -9.8 m/s 2, so it is going to be constant -- then that ball is going to come in contact with the floor.1551

                            Its acceleration is going to change very quickly and then it is going to be in -- we call free-fall -- again.1559

                            It is going to be in the air with no other forces on it.1565

                            It is going to have a constant 9.8 m/s 2 again.1568

                            All right. How can we start to fill these in?1572

                            Well, when the ball hits the ground, its acceleration is going to be positive for a second.1575

                            It has to be in that direction to change its velocity.1582

                            So we are going to have to have a spike in our acceleration time graph.1584

                            For our velocity graph, it is going to start at 0 and it is going to go faster and faster and faster.1591

                            Then, when it hits the ground it is going to have a spike.1596

                            It is going to have a very high velocity as it sways back up, slowing down, slowing down, slowing down -- stopping.1599

                            And finally, as we look at the position of the basketball -- if we take a look, we have to have some sort of path that allows the ball to do that to come back up to Bobbie's hand.1608

                            So that is a pretty in-depth example and much more complicated example of how you can put position, velocity, and acceleration all together to make one complete story for what is happening to an object.1621

                            All right, let us do another one.1633

                            Draw the velocity time graph for a ball tossed upward which returns to the point from which it was tossed.1636

                            Well, I am going to start off by making my axis again. This is going to be a velocity time graph.1643

                            If we toss something upwards -- like throw it up -- the moment it leaves my hand, it has its biggest velocity. Right?1653

                            It's positive -- slowing down, slowing down, slowing down, slowing down -- stops for a split second, switches directions, speeds up, speeds up, speeds up, speeds up, speeds up, but in the negative direction.1661

                            So if it starts off with its biggest velocity -- it could be there -- a little bit later at its highest point, for a split second it stops, then it goes faster, and faster, and faster in the opposite direction.1672

                            So the velocity time graph for that situation would look something like that.1685

                            All right, let us take a look at one last example.1693

                            How can we get displacement from a velocity time graph?1696

                            The graph below shows the velocity of an object travelling in a straight line is a function of time.1700

                            Determine the magnitude of the total displacement of the object at the end of the first 6 s.1705

                            So we have a velocity time graph -- we want displacement. Right away you should be thinking area.1711

                            Velocity time graph wants displacement -- you need to take the area.1717

                            So at 6 s, we will draw our line there.1720

                            We need the area of everything under the graph to the left of that.1723

                            Again, a couple of ways you can do this -- but the easiest way I see it off the top of my head is to break this up into a triangle and a rectangle.1729

                            The area under that should give us the total displacement.1741

                            So we have the area of the triangle, 1/2 base times height or 1/2 times our base 2 s times our height of 10 m/s is going to be 1/2 x 2 x 10 -- 10 and seconds versus seconds in the denominator -- meters.1745

                            And the area of our rectangle, length times width, or from 2 to 6 s is 4 s times its height -- 10 m/s -- seconds over seconds cancel out -- 40 m -- so the total displacement then, I just add those two up, 40 + 10 -- 50 m.1767

                            Hopefully, that gets you started with some of these quantities that describe motion and motion graphs, particle diagrams, position time diagrams, velocity time diagrams, acceleration time diagrams -- gets you started, gets you going.1791

                            I definitely recommend some more practice on your own.1804

                            Thanks for watching Educator.com. We will be back soon. Make it a great day!1807

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