Home » Physics » AP Physics 1 & 2 » Kinematic Equations

Dan Fullerton

Dan Fullerton

Kinematic Equations

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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
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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

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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

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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

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

5m 17s

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Question 1
0:21
Question 2
1:01
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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
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Question 1
0:19
Question 2
1:05
Question 3
2:09
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2:53
Question 5
3:17
Question 6
4:00
Question 7
4:41
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5:20
Momentum & Impulse

9m 29s

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6:57
Question 9
7:47
Conservation of Momentum

9m 33s

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0:15
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2:08
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4:03
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4:10
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6:08
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6:55
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8:26
Work & Power

6m 2s

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0:29
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0:55
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1:36
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3:22
Question 7
4:01
Question 8
4:18
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4:49
Springs

7m 59s

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

7m 6s

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0:10
Question 2
1:03
Question 3
1:32
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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

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

4m 11s

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0:51
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1:30
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2:19
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3:12
Electric Potential

5m 12s

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

6m 54s

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0:42
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2:01
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3:02
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3:52
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4:15
Question 7
4:37
Question 8
4:59
Question 9
5:50
Resistance

5m 15s

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

4m 27s

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

6m 36s

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

3m 43s

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0:16
Question 2
0:31
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0:56
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1:19
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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
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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

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Question 1
0:13
Question 2
0:40
Question 3
1:04
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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 (52)

2 answers

Last reply by: Professor Dan Fullerton
Mon Feb 3, 2020 6:39 AM

Post by Elijah Zaito on February 2, 2020

For example 7 under Kinematic Equations (falling objects around 27:50 into Kinematics) - I see how you solved for the 45 m, but when trying to do the problem manually, I was getting 60 m.  

To clarify, I mean to say that if gravity acceleration is 10 m/s^2 and the brick falls for 3 seconds with no air resistance, wouldn't that mean that the brick was going 10 meters per second for Second 1, then 20 m/s for Second 2, and finally 30 m/s for Second 3 (accelerating at 10 meters per second, each second)?

Adding these up, I got 60 meters traveled in 3 seconds. I know I am missing something here on why they do not match when using the equation or doing it manually. Any help would be appreciated!

1 answer

Last reply by: Professor Dan Fullerton
Tue Sep 18, 2018 5:27 AM

Post by Kevin Wang on September 17, 2018

Hi Dan, are there any extra practice problems for these kinematic equations

Thanks

2 answers

Last reply by: Professor Dan Fullerton
Tue Aug 29, 2017 9:09 AM

Post by Carlins Almonor on August 29, 2017

My teacher often gives questions that consists of a collision type problem. For example, a car is driving at a certain velocity and sees a barrier at some distance away. Given that his reaction time is some amount of seconds and he accelerates at some amount in the opposite direction, would he crash or not crash?

3 answers

Last reply by: Professor Dan Fullerton
Thu Mar 16, 2017 5:14 PM

Post by Woong Ryeol Yoo on March 15, 2017

Referring to the "AP style" problems in the back of the AP Physics 1 Essential 2nd edition, I have a problem with #7 in page 325.

So, I understand that we can use kinematics equation to find the acceleration. But, the answer (0.855) seems to be only valid for one kinematics equation. I used other equations that have velocities by plugging in the velocities I found by doing displacement over time. But, every equation gave me different answers? Why is this? Is there something wrong with the problem?

4 answers

Last reply by: Professor Dan Fullerton
Tue Nov 29, 2016 8:11 PM

Post by Prajwal Jagadish on November 29, 2016

In the high school physics course, the equations the professor gave us were somewhat different. Are these just different forms?

2 answers

Last reply by: Zhe Tian
Sun Sep 6, 2015 1:32 PM

Post by Zhe Tian on September 5, 2015

Ignore my previous Q, would delete it or edit if I could. A better question would be would it matter if I make down negative? On both the astronaut question and example 10 ball thrown down, I made down my negative and ended up with the exact answer except negative. Obviously the negative and positive answers are different, so does that mean down should always be positive or on the AP there would be +/- answers?

1 answer

Last reply by: Professor Dan Fullerton
Sat Sep 5, 2015 7:43 PM

Post by Zhe Tian on September 5, 2015

On the astronaut example, why wouldn't the distance be negative? I thought if an object was falling down, the distance would have to be negative?

1 answer

Last reply by: Professor Dan Fullerton
Fri Aug 28, 2015 6:48 AM

Post by Bilbo Baggins on August 27, 2015

Hello, is there a place where I could find each physics equation with its components explained? For example, this video explained that a variable with a line over it was average. Thanks

1 answer

Last reply by: Professor Dan Fullerton
Tue Jun 2, 2015 7:37 PM

Post by Vinu Gowda on June 2, 2015

In the fall, I am taking Engineering physics, so if I watch your videos?
Does it help for me?

1 answer

Last reply by: Professor Dan Fullerton
Tue May 26, 2015 2:10 PM

Post by Denise Aguilar on May 26, 2015

Hello Professor,
Kind of a silly question, but in part c of example five  when changing the kin. eq to solve for a how did the 2 come in for 2 delta x over t squared? I am sure it is a simple algebraic move.
Thanks

2 answers

Last reply by: Professor Dan Fullerton
Tue Nov 11, 2014 10:05 AM

Post by TAHA sakor on November 11, 2014

What do you mean in (delta y)

2 answers

Last reply by: robert moreno
Tue Jul 1, 2014 6:22 PM

Post by robert moreno on June 21, 2014

This is not pertaining to the lecture, but where do I go to find more practice problems?

3 answers

Last reply by: Professor Dan Fullerton
Fri Dec 20, 2013 7:36 AM

Post by Hyun Cho on December 18, 2013

i got a question.  at 13:10 about the astronaut problem,i initially set the downward direction as negative and i got -1.65m/s2 as the acceleration.  on the AP test, will i still get credit for the answer as long as i say " I have set downward as negative" in my answer? and what would i do for the multiple choice? is there some kind of direction convention that i m not aware of? thanks

1 answer

Last reply by: Professor Dan Fullerton
Sun Sep 15, 2013 6:27 AM

Post by Constance Kang on September 14, 2013

Hello for example 5 part C why can't u use average velocity (0.3m/s) over time (0.3 s) to find acceleration?

1 answer

Last reply by: Professor Dan Fullerton
Thu Sep 12, 2013 5:47 AM

Post by Constance Kang on September 11, 2013

Hi, just find something odd when deriving the second kinematic equation. since displacement=vt i plug in v=(v0+at) --> displacement= (v0+at)t=v0t+at^2  instead of (v0+1/2at^2   why is this?

1 answer

Last reply by: Professor Dan Fullerton
Thu Aug 22, 2013 11:38 AM

Post by Larry wang on August 22, 2013

Hello once again! On your slide about "Air Resistance", from the second bullet point we understand that objects fall at the same rate. Does that mean regardless of objects' masses they fall at the same time. What kind of rate we are taking about over here: acceleration/velocity? Thank you!

1 answer

Last reply by: Professor Dan Fullerton
Fri Aug 16, 2013 8:40 AM

Post by Marie Romano on August 16, 2013

Hi Mr. (Professor?) Fullerton,

I have just started going through these to review for my college physics courses to strengthen my physics. This is probably not calculus-based, right? If it isn't, will there ever be a possibility of YOU teaching a calculus based physics lectures? Because that would just make my life happy.

Thank you for being an excellent teacher- I know how powerful and influential a good teacher can be in a student's life.

Sincerely your student,
-Marie

1 answer

Last reply by: Professor Dan Fullerton
Wed May 22, 2013 11:16 AM

Post by Jude Nawlo on May 22, 2013

Hi Mr. Fullerton,

Thank you for your outstanding Physics Lectures. I have one question about determining the final speed of an object in free fall. If an object is actually physically thrown downwards from a given height with a given speed (e.g. 5 m/s), then from what I understand a would equal 9.8 and vi would equal 5, since they are both positive and in the same direction. But would the displacement then be negative in that free fall scenario, if it is travelling downwards? I have been solving problems using a positive value for displacement in the v^2 = vo^2 + 2ax equation and using the concepts from this lecture, and I have been getting them right, but have been confused now that I realize I have not been using a negative value for displacement. Is this reasoning faulty?

1 answer

Last reply by: Professor Dan Fullerton
Thu May 9, 2013 12:54 PM

Post by Nawaphan Jedjomnongkit on May 9, 2013

In example 10 , Do we need to check that in 0.7 second will the ball touch the ground first because it has information about the height that we throw the ball. Lets say if the time more than 0.7 and the ball actually bounce up then v cannot find from that formula right?

1 answer

Last reply by: Professor Dan Fullerton
Tue Mar 26, 2013 9:14 AM

Post by Ranier Camarines on March 26, 2013

awesome!!

Related Articles:

Kinematic Equations

  • The kinematic equations can be used to solve kinematics problems in which acceleration is constant.
  • When you know three of the five kinematic quantities for constant acceleration, you can use the kinematic equations to solve for the other two.
  • You can avoid quadratics by solving for an intermediate quantity, simplifying your calculations.
  • Free fall is a condition in which the only force acting on an object is the object's weight.
  • The acceleration due to gravity on the surface of the Earth, a constant known as g, is approximately 9.8 m/s^2, which can be approximated as 10 m/s^2 to simplify calculations. This is also known as the gravitational field strength.
  • The motion of an object in free fall which travels up and then back down is symmetric.
  • The motion of a free falling object which travels up and then back down can be broken down into motion on the way up, then motion on the way down, which may simplify calculations.
  • At the highest point of its path, a free falling object's vertical velocity is 0.

Kinematic Equations

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.

  • Intro 0:00
  • Objectives 0:07
  • Problem-Solving Toolbox 0:42
    • Graphs Are Not Always the Most Effective
    • Kinematic Equations Helps us Solve for Five Key Variables
  • Deriving the Kinematic Equations 1:29
  • Kinematic Equations 7:40
  • Problem Solving Steps 8:13
    • Label Your Horizontal or Vertical Motion
    • Choose a Direction as Positive
    • Create a Motion Analysis Table
    • Fill in Your Givens
    • Solve for Unknowns
  • 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
  • Air Resistance 24:51
    • Drop a Ball
    • Remove the Air from the Room
    • Analyze the Motion of Objects by Neglecting Air Resistance
  • Acceleration Due to Gravity 25:22
    • g = 9.8 m/s2
    • Approximate g as 10 m/s2 on the AP Exam
    • G is Referred to as the Gravitational Field Strength
  • Objects Falling From Rest 26:15
    • Objects Starting from Rest Have an Initial velocity of 0
    • Acceleration is +g
  • Example 7: Falling Objects 26:47
  • Objects Launched Upward 27:59
    • Acceleration is -g
    • At Highest Point, the Object has a Velocity of 0
    • Symmetry of Motion
  • 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

Transcription: Kinematic Equations

Hi everyone and welcome back to Educator.com. I'm Dan Fullerton.0000

And now I would like to talk about kinematic equations.0004

Kinematic equations are used to solve problems for objects moving at a constant acceleration in a straight line, or for multiple dimensional problems when we start adding different kinematic equations for different dimensions.0007

Our goal is going to be to solve problems for objects moving at a constant acceleration in free fall and in straight lines.0019

If it is not constant acceleration, we are not going to be able to use these equations.0026

However, just about every problem you are going to see on the AP exam has to do with the constant acceleration.0031

So these are very, very useful for the AP course.0037

Now what we are really doing is talking about another way to solve problems.0042

You can solve all of these problems by making motion graphs like we talked about previously.0046

But they are not always the most effective or efficient way of understanding motion.0051

The kinematic equations help us solve for the five key variables -- they are going to describe the motion of an object in a single dimension -- V0 or V initial, initial velocity; V or V final, the final velocity; displacement δx, or if it is in the y direction, δy; the acceleration, the change in velocity; and the time.0056

Those five key quantities are what we need to know to understand what is happening to the motion of an object in a constant acceleration scenario.0077

So let us see if we cannot derive these kinematic equations.0088

As I go through this, realize you do not have to repeat it, but I would like you to do everything you can to try and follow along with the derivation because I think it is important that you understand where these are coming from.0093

So we are going to take the motion of an object that starts at some initial velocity, V0, and accelerates with a constant acceleration to some final velocity, V, in some amount of time, t.0103

So there is our time, t, and what we are going to do first to get our first equation is we are going to start with the definition of acceleration.0119

Acceleration is the change in velocity divided by time, or that will be V final - V initial/time.0126

With a little bit of rearrangement we can say that the V - V0 = acceleration x time, or V final = V initial + acceleration x time.0136

There is our first kinematic equation.0152

All right, now what we are going to do next is looking at this graph -- we can find V -- change in an object's position that changes its displacement by taking the area under the velocity-time graph.0156

So what we are going to do there is we are going to say that the change in the object's position is the area.0167

To get the area, I am going to break this up into a rectangle and a triangle.0175

The area of our triangle is 1/2 base x height and we have the area of our rectangle, length x width.0181

So as we look at our triangle, that is going to be 1/2 x base, that is T, and the height of our triangle right here is going to be V - V initial, and we have to add in our rectangle, V0 x T.0190

This implies then, since we already know that V = V0 + AT -- we just learned it up there.0211

We could rearrange this to say that V - V initial = AT.0222

I am going to replace V - V initial here with AT.0227

So I then get δx = 1/2T x AT + V0T, or with a little bit of Algebra, I can show that δx = V0T + 1/2AT2.0232

There is our second kinematic equation.0258

Now the next step is I am going to come back up here and I am going to go from δx and pull that step back.0264

So we are going to write down δx = 1/2T, V - V initial + V initialT.0271

I am going to start there and just take a slightly different derivation to come up with our next kinematic equation -- our next tool in our toolbox for solving problems.0282

When I do that then, if I start multiplying this out, I get 1/2VT - 1/2V0T + V0T.0292

That implies then that δx = -- I have 1/2VT and -1/2V0T + V0T is just going to be +1/2V0T.0303

If I divide everything by T, I then determine that δx/T = V - V0/2.0316

But realize now δx/T -- that is your average velocity here.0328

So average velocity equals -- Oops that is a positive, that is a plus, plus, plus -- Vaverage = V + Vinitial/2.0332

The average velocity for something with constant acceleration, you take the initial, you take the final, you go halfway in between them.0343

There is another kinematic equation -- another useful tool.0350

Let us go back now to average velocity = δx/T and let us rearrange that to say that δx = Vaverage x T.0356

But we just said that Vaverage is V + V initial/2, so that is going to be V + V initial/2 x T.0369

Now in this next step, we are going to have to go back to some of the stuff we have derived previously.0380

We know V = V0 + AT, therefore we could rearrange this to say that T = V - V0/A.0385

So as I write this again, δx = V + V initial/2 and I am going to replace T here with V - V0/A.0396

This implies then that δx is going to be equal to, -- well now with a little bit of math -- we are going to have V2 - V0V + V0V -- that makes 0 - V02/2A.0415

With a little bit of rearrangement, V2 - V02 = 2Aδx or one more step, V final2 = V initial2 + 2Aδx -- V2 = V initial2 + 2Aδx.0433

So our kinematic equation is -- just to clean these up -- V final = V initial + AT, δx = V initialT+ 1/2AT2, V2 = V initial2 + 2Aδx.0456

And we also threw in there and mentioned that Vaverage = V final + V initial/2 -- the average of those two, and that one is oftentimes neglected because that is more of a common sense one.0471

But all of these work for situations of constant acceleration.0482

Now let us talk about some problem solving steps that will allow you to solve a ton of kinematic equations.0494

What we are going to do is we are going to label the axis for horizontal or vertical motion.0500

When we do that, we are going to pick a direction to be positive.0504

Typically, I like to pick the direction the object is moving initially, but it really does not matter as long as you are consistent within the problem.0507

We are going to create a motion analysis table, where we are going to have V initial, V, δx or y, A, T, and we are going to fill in all the information we are given.0514

When we know any three items in that table, we can solve for the unknowns.0524

Let us see how this works.0530

A race car starting from rest -- starting from rest -- V initial = 0, accelerates uniformly at a rate of 4.9 m/s2. There is our acceleration.0532

What is the car's speed after it has traveled 200 m?0544

All right, well I am going to say it is going to the right and we will call that the positive x direction and I will make my motion table -- V initial, V, δx, A, and T and fill in what I know.0548

V initial = 0 -- I know acceleration is 4.9 m/s2.0563

What is the car's speed after it has traveled 200 m -- that must be our displacement.0570

I know three things in the table -- I can always solve for the other two using my kinematic equations.0575

So I look for a kinematic equation that has all or most of these in it.0581

I want to know the car's final speed.0585

I am going to choose then, V2 = V initial2 + 2Aδx because I want V -- that is there -- I want V initial, I have it -- I need A, I have A and δx.0590

It should work out pretty well.0606

Next, if I want to know its speed, I am going to substitute in my values, V initial, 02 + 2 x A, 4.9 m/s2, x δx, 200 m.0610

Therefore I can say that V2 = 2 x 4.9 x 200 or 1960 m2/s2.0626

But I want just velocity, not velocity2, so I take the square root and say that V must equal the square root of 1960 which is +/-44.3 m/s.0636

Now I have to use a little common sense to figure out which root I want, the positive or the negative, and it should be pretty obvious to see that I want the positive root.0648

The car is not going to accelerate in one direction and then have a velocity in the opposite direction in this case.0655

So my answer, final velocity must be 44.3 m/s.0662

Let us take a look at one that is traveling in the vertical direction.0674

An astronaut standing on a platform on the moon drops a hammer.0678

If the hammer falls 6 m vertically in 2.7 s, what is its acceleration?0680

All right, as we start again, we have our object.0687

It is going to travel down, so we will call down the positive y direction -- that is the direction that it is traveling initially.0691

Let us make our motion table.0697

V initial, V, δy, A, T, -- and if they drop the hammer -- initial velocity -- when you drop something is 0.0700

The hammer falls 6 m vertically, 6 m in a time of 2.7 s.0711

What is its acceleration?0719

So we are looking for A -- we know three things -- we should be able to get there.0720

We have to pick the right kinematic equation now, and I am going to pick δy = V initialT + 1/2AT2.0725

And what is really nice in this scenario is if you see V initial = 0, well 0 x anything is 0, so that whole term goes away and becomes 0.0738

So this term becomes δy = 1/2AT2.0747

I am solving for A so if I multiply both sides by 2, 2δy = AT2 and divide both sides by T2, that would imply then that A = 2δy/T2.0754

Substitute in my variables, 2 times δy, 6m over T2, 2.72, so 12/2.72 should give me about 1.65 m/s2 as the acceleration of the hammer dropped on the moon.0770

And the acceleration due to gravity on the moon is somewhere in the ballpark of 1.6 m/s2, about 1/6th that of Earth, so that makes sense. Great!0794

Let us take a look at the two-step problem.0805

A car traveling on a street road at 15 m/s accelerates uniformly to a speed of 21 m/s in a time of 12 s.0808

Find the total distance traveled by the car in this 12 s time interval.0816

Well, let us assume that it is going to the right again and we will call that our positive x direction.0821

But as we do that, let us go make our motion table again -- V initial, V, δx, A and T.0824

V initial = 15 m/s -- it accelerates to a speed of 21 m/s -- that is going to be our final velocity, in a time of 12 s.0836

Find the total distance traveled by the car in this 12 s interval.0848

Right away as I look at this -- do I have any equations that will allow me to get δx with both V's and T?0854

Well not right away, but there are a couple of things that we could do.0863

One thing is we could look at that kinematic equation, Vaverage = V initial + V final/2, which is going to be 15 + 21/2 or 18 m/s.0867

Since we can treat this as the average velocity for the entire time interval, we know that average velocity = distance/time, therefore, the distance traveled will just be Vaverage x time, or 18 m/s x our time of 12 s -- 18 x 12 = 216 m.0882

But there are other ways to solve this problem too.0908

We could go and solve for A first if we did not want to use that formula.0912

A = δV/T which is V final - V initial/T.0916

That shall be 21 m/s - 15m/s / 12s or 0.5 m/s2.0923

We know one more thing, now we can use any equation we want to get δx.0934

Let us say we want to δx = V initialT + 1/2AT2.0940

That will be 15 m/s x 12 s + 1/2 x A, 0.5, T2, 12 s2) -- again it comes out to 216 m.0948

Or we could have even gone and done V2 = V initial2 + 2Aδx.0967

Therefore δx must be V2 - V initial2/2A or 212 - 152/2xA, 1/2, which again comes out to be 216 m.0976

Many different routes to the same conclusion, to the same answer.0998

Let us take a look at an acceleration problem.1003

How long must a 5 kg kitty cat accelerate at 3 m/s2 in order to change its velocity by 9 m/s?1007

Well to do this one we will start off by listing what we know.1015

V initial, V, δx, A and T and what we know here is δv, the change in velocity, is going to be 9 m/s.1020

We do not know specifically V initial or V, but it tells us that A = 3 m/s2, and we want to know the time.1030

Well right away, I would jump to acceleration = δV/T, which will be 9 m/s over -- pardon me --1041

I am looking for time, so I have to solve for T first, which implies then that T = δV/A which will be 9 m/s/3 m/s2 -- 9/3 = 3 m/s/m/s2 -- 3 s.1052

All right. Let us take a look at one that uses a particle diagram.1074

A spark timer -- one of those things that goes "ta-ta-ta-ta-ta" at regular intervals is used to record the position of a lab cart accelerating uniformly from rest.1080

Every 0.1 second the timer marks a dot on a recording tape to indicate the position of the cart at that instant, as shown.1090

We have a ruler and there is our tape. Find the displacement of the cart at time, T = 0.3 s.1097

To begin with, if we want the displacement of the cart, this must be 0.1 s -- 0.2 s -- 0.3 s.1103

All I am going to do there is I am just going to find the displacement by looking up here at my ruler and saying that the displacement there must be pretty close to 9 cm.1114

Now to find the average speed of the cart from 0 - 0.3 s.1125

In that case, if we want the average speed of the cart, Vaverage = δx/T, Which is going to be 0.09 m/time of 0.3 s which is going to be 0.3 m/s.1131

What is the acceleration of the cart?1155

To find the acceleration of the cart, now we have to go back to our kinematics.1157

I would use δx = V0T + 1/2AT2, because we know that V initial, V0 right here is 0 so that term goes away.1162

This implies then that A = 2δx/T2 or 2 x 0.9 m/our time, 0.3 s2 which will give us an acceleration of 2 m/s2.1172

And finally, it asks us on the blank diagram, draw at least 4 dots indicating a cart moving at constant velocity.1193

All right, all I need to do is make sure that my dots are evenly spaced -- then it is moving at constant velocity.1202

Nice review of particle diagrams.1210

Let us take a look at a kinematics problem that may require a quadratic solution.1213

Arnie the aardvark accelerates at a constant 2 m/s2 from an initial velocity of 1 m/s.1217

How long does it take Arnie to cross a distance of 50 m?1224

Well we have V initial = 1 m/s.1228

We do not know final velocity -- δx is going to be 50 m -- it tells us that acceleration is 2 m/s2 and we are asked to find the time -- How long?1233

To pick a kinematic equation that has those four quantities in it, I am going to write δx = V initialT+1/2AT2.1249

Now δx = 50, so that is going to be equal to V initial 1T or T + 1/2 x A2 x T2, therefore 50 = T + T2.1260

That is starting to look like a quadratic equation.1279

What I am going to do is to rearrange that to fit the form of the quadratic formula T2 + T - 50 = 0.1282

Now we can apply the quadratic formula where T = -V+/- the square root of V2 -4AC/2A.1294

Or that is going to be -- well our B is going to be 1, so that is going to be -1 +/- the square root of 12-4 x A, which is 1 x C -- -50/2 x A which is 1.1300

With a little bit of math there, that will be -1 + 14.18/2 or -1 - 14.18/2, which gives us choices of T being equal to either 6.59 s or -7.59 s.1334

Which one makes sense? Well of course, it is that positive time.1360

Now having gone through that, that quadratic formula is a lot of work and very prone to error.1367

So what I would recommend here is if you get to the point where you have a quadratic formula solving for T, solve for the other variable first using kinematic equations, then go solve for T.1371

You can avoid using the quadratic.1381

So the alternate solution -- the way I would typically do this problem to avoid all of that extra math is I would solve for V first using V2 = V initial2 + 2Aδx.1386

V initial2 -- that will be 12 + 2 x A, 2, x δx -- 50 -- so we will find then that V2 = 201 m/s2, therefore V = 14.18 m/s.1399

Now with that, we can go back to another kinematic equation -- any of them we want to get T -- I am just going to use V = V0 + AT.1420

So, let us rearrange that to say that T = V - V0/A which is 14.18 m/s - V initial -- 1 m/s/acceleration -- 2m/s2 and of course I will come out with the same answer, 6.59 s.1431

It is the same thing we had before, but I was able to avoid that quadratic formula and those extra complications.1453

A nice way to simplify the math.1460

Let us talk about free fall.1464

When the only force acting on an object is the force of gravity -- the object's weight -- another name for the force of gravity -- we refer to the object's motion as free fall.1466

This includes objects that have a non-zero initial velocity.1476

So free fall can be something that I throw up in the air, could be something I drop or that I throw down.1479

It does not matter as long as the only force acting on it is gravity.1484

As we talk about this, everybody likes to ask about air resistance.1492

If you drop a ball and a sheet of paper, for example, it is obvious that they do not fall at the same rate.1496

If you could remove all the air from the room, however, you will find that they do fall at the same rate.1500

You will analyze the motion of objects in this course almost always by neglecting air resistance, which is a form of friction.1506

Later on we can add it back in, but for the purposes of this course keeping things simple for now, we are going to neglect air resistance.1513

Let us talk about the acceleration due to gravity.1521

Near the surface of the earth, objects accelerate downward at a rate of 9.8 m/s2.1524

This is such an important number, that in Physics, we call this acceleration little 'g'.1531

For the purposes of the AP exam, we can approximate that as 10 m/s2 to make the math more simple.1537

Save us some time, you will still get full credit for all of your solutions.1544

More accurately though, g is actually referred to as the gravitational field strength.1548

When we get into gravity, we will talk about how we could calculate that -- what that means in a little more depth.1553

Now as we move further away from earth, g decreases.1558

If you were on another planet, g would be different.1560

But on the surface of the Earth, it is 9.8 m/s2 and to make the math easy we can call it 10.1566

Let us talk about objects falling from rest.1575

Objects starting from rest have an initial velocity of V0 of 0 -- falling from rest -- drop it -- initial velocity is 0.1578

Since the object's initial motion is down, I like to call down the positive direction when I am setting out my kinematic equations.1587

The acceleration then, if we are calling down the positive direction, the object accelerates in the same direction, so the acceleration then would be positive g.1594

Let us take a look at an example for a falling object.1606

How far will a brick starting from rest fall freely in 3 s? Again we are going to neglect air resistance here.1611

Well if it is falling, I am going to call down the positive y direction.1617

I am going to set up my kinematic equations table -- V initial, V, δy, A and T.1621

If it is falling from rest, V initial = 0 -- It falls for 3 s and I need to know one more thing.1630

Acceleration due to gravity is +g which I am going to approximate as 10 m/s2.1637

So define how far I am looking for δy, I will use the equation δy = V initialT + 1/2AT2.1645

Then use that favorite trick where V initial = 0 -- that term goes away.1655

So δy = 1/2xA, 10, x time -- 32. That is going to give us 45 m.1660

Objects falling from rest.1675

On the other hand, we can launch objects upward.1677

We have to examine the motion of the object on the way up and the way down though.1680

Since the object's initial motion is up, I am going to call that my positive y direction and if up is my positive y direction, my acceleration is the opposite direction of what I called positive so the acceleration would be negative g.1685

I know that at the highest point of motion, if I throw anything up and it comes back down -- at its highest point for the split second -- its velocity is 0.1698

And we have some symmetry of motion there.1706

If I throw up an object for 2 s, it will take 2 s to come back down.1710

If I throw it up with an initial velocity of 10 m/s up -- when it gets right down to the same height, it will be going 10 m/s down.1715

There is a symmetry of motion involved here.1723

So let us take a look at another example. Now we are going to throw a ball upward.1727

A ball thrown vertically upward reaches a maximum height of 30 m above the surface of the earth.1733

Find the speed of the ball at its maximum height.1736

Well right away I am going to call up the positive y direction.1739

Before I get any further it says find the speed of the ball at its maximum height -- a trick question.1743

For the highest point for any object going up and down for a split second, its speed is 0.1750

So the answer at that point is V = 0. You did not even have to do any math there.1765

How about the height of a jump?1774

A basketball player jumps straight up to grab a rebound.1775

If she is in the air for 0.8 s, how high does she jump?1778

Well, here is our basketball player -- jumps up for a split second at highest point -- stops -- comes back down.1782

That entire trip, up and down, took 0.8 s and we know time to go up is 0.4 s and the time to go down is 0.4 s, so that time is 0.4 s.1791

We also know at the highest point that the velocity of the basketball player for a split second is 0.1795

So we can analyze this in a couple of different ways.1802

Let us analyze the basketball player's jump on the way up.1806

Let us just look at that part of the motion, the way up.1810

So on the way up, let us call up the positive direction.1814

We have V initial, V, δy, A and T.1817

We do not know initial velocity, but we know that final velocity on the way up is 0 because we are only looking for this 0.4 s time interval -- so half the time, 0.4 s to go up.1824

We also know if we called up the positive y direction that A is -10 m/s2.1835

Now if we want to figure out how high she jumped -- to what her displacement was at this 0.4 s, I could do this in a number of ways.1841

But why don't I start with finding her initial velocity -- V = V0 + AT, that will save me a quadratic, which implies that V initial = V - AT.1850

This implies that V initial then is going to be V(0) - A(-10) x T(0.4) -- Negative x negative = positive. 10 x 0.4 = 4 m/s.1866

Now I can use δy = V0T + 1/2AT2.1887

Since I know V0 now -- it is 4 m/s -- that is going to be 4 x 0.4 + 1/2 x A(-10) x T2 (0.4)2.1896

So δy -- when I do the math -- plug that into my calculator, I come up with about 0.8 m. About that high.1910

Let us try an alternate path to the solution though.1921

Let us look and analyze the solution on the way down.1924

So on the path down, I am going to assume that this is the same as if we had dropped an object from rest up here at this point.1929

We will call down the positive y direction -- V initial now is 0 -- we do not know final velocity right before she hits the ground -- Well, we would if we used our symmetry of motion, but let us pretend we just took this path.1935

Δy is what we are trying to find.1949

A is now +10, since we called down the positive direction and our time is 0.4 s.1952

We can use δy = V initialT + 1/2AT2.1960

V initial is 0 so that term goes away -- this becomes 1/2 x A(10), x T2 (0.4)2 or again, 0.8 m.1969

And of course we should get the same answer because we have that symmetry of motion.1983

How about a ball thrown downward?1989

A ball is thrown straight downward with a speed of half a meter per second from a height of 4 meters.1994

What is the speed of the ball, 0.7 s, after it is released?1997

Well, if we called down the positive y direction, we have V initial, V, δy, A and T -- where V initial is now 0.5 m/s -- that is positive because we said down was positive -- A = 10 m/s2 and we want the speed 0.7 s after it was released.2002

I can jump right to V = V initial + AT which is going to be 0.5 + A(10) x T(0.7) -- 0.5 + 10 x 0.7 = 7.5 m/s2.2027

Let us try one last simple problem just to make sure we have got it. Find the maximum height.2055

A quarter-kilogram baseball is thrown upward with an initial speed of 30 m/s.2061

Neglecting friction, no air resistance, the maximum height reached by the baseball is approximately what?2067

So we are looking for a displacement here.2071

All right, we are going to call up the positive direction because that is the way the ball goes initially.2074

Our initial velocity is 30 m/s -- final velocity when it reaches its highest point must be 0 -- another known that we have there.2080

We are trying to find δy.2090

Acceleration is -10 m/s2. Negative because we called up positive and the acceleration due to gravity is down, and we do not know time.2094

Let us choose a kinematic equation that is going to help us out.2104

I want δy so I am going to use V2 = V initial2 + 2Aδy.2107

Let us rearrange this for δy and I get V2 - V initial2/2A.2116

Therefore, δy = V2, that is going to be 0 - V initial2(30)2/2 x A(-10).2125

That is going to be -900/-20, or 45 m.2141

Kinematic equations are terrific tools for problem solving, but you have to remember that they can only be used in situations of constant acceleration.2151

Make that table with V initial, V, δx or δy, A and T, and when you know three of those quantities you can always solve for the other two.2158

Hopefully that gets you a great start.2168

Thanks for watching Educator.com. Make it a great day!2170

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