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Center of Mass, Part 2

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  • Intro 0:00
  • Motion of a System of Particles 0:53
    • Position Vector of Center of Mass
    • Total Momentum
    • Net Force Acting on a Particle
  • Exploding a Projectile 19:12
    • Shooting a Projectile in x-z Plane
    • Projectile Explodes into 2 pieces of Equal Mass
  • Rocket Propulsion 35:09
    • Rocket with Mass m and Velocity v
  • Rocket in Space 53:39
    • Rocket in Space with Speed=3000m/s
    • Engine is Turned On
    • Final Mass=1/2 Initial Mass
    • Speed after Fuel is Burned
  • Extra Example 1: Ball Inelastic Hits Other Ball
  • Extra Example 2: Rocket Launch Thrust
Professor Jishi

Professor Jishi

Center of Mass, Part 2

Slide Duration:

Table of Contents

Section 1: Mechanics
Introduction to Physics (Basic Math)

1h 17m 37s

Intro
0:00
What is Physics?
1:35
Physicists and Philosophers
1:57
Differences Between
2:48
Experimental Observations
3:20
Laws (Mathematical)
3:48
Modification of Laws/Experiments
4:24
Example: Newton's Laws of Mechanics
5:38
Example: Einstein's Relativity
6:18
Units
8:50
Various Units
9:37
SI Units
10:02
Length (meter)
10:18
Mass (kilogram)
10:35
Time (second)
10:51
MKS Units (meter kilogram second)
11:04
Definition of Second
11:55
Definition of Meter
14:06
Definition of Kilogram
15:21
Multiplying/Dividing Units
19:10
Trigonometry Overview
21:24
Sine and Cosine
21:31
Pythagorean Theorem
23:44
Tangent
24:15
Sine and Cosine of Angles
24:35
Similar Triangles
25:54
Right Triangle (Opposite, Adjacent, Hypotenuse)
28:16
Other Angles (30-60-90)
29:16
Law of Cosines
31:38
Proof of Law of Cosines
33:03
Law of Sines
37:03
Proof of Law of Sines
38:03
Scalars and Vectors
41:00
Scalar: Magnitude
41:22
Vector: Magnitude and Direction
41:52
Examples
42:31
Extra Example 1: Unit Conversion
-1
Extra Example 2: Law of Cosines
-2
Extra Example 3: Dimensional Analysis
-3
Vector Addition

1h 10m 31s

Intro
0:00
Graphical Method
0:10
Magnitude and Direction of Two Vectors
0:40
Analytical Method or Algebraic Method
8:45
Example: Addition of Vectors
9:12
Parallelogram Rule
11:42
Law of Cosines
14:22
Law of Sines
18:32
Components of a Vector
21:35
Example: Vector Components
23:30
Introducing Third Dimension
31:14
Right Handed System
33:06
Specifying a Vector
34:44
Example: Calculate the Components of Vector
36:33
Vector Addition by Means of Components
41:23
Equality of Vectors
47:11
Dot Product
48:39
Extra Example 1: Vector Addition
-1
Extra Example 2: Angle Between Vectors
-2
Extra Example 3: Vector Addition
-3
Dot Product and Cross Product

1h 6m 17s

Intro
0:00
Dot Product
0:12
Vectors in 3 Dimensions
1:36
Right Handed System
2:15
Vector With 3 Components (Ax,Ay,Az)
3:00
Magnitude in 2 Dimension
3:59
Magnitude in 3 Dimension
3:40
Dot Product of i*i
7:21
Two Vectors are Perpendicular
8:50
A.B
13:34
Angle Between Two Vectors
17:27
Given Two Vectors
17:35
Calculation Angle Between Vectors with (A.B)
18:25
Cross Product
23:14
Cross Product of AxB
23:42
Magnitude of C=AxB cos Theta
24:35
Right Hand Rule
27:07
BxA
28:40
Direction of IxJ=K
31:04
JxK
33:15
KxI
35:00
Evaluation in Terms of Determinants
39:28
Two Vectors A and B with Magnitude and Direction
39:35
Calculate AxB
40:08
Example
49:59
Extra Example 1: Perpendicular Vectors
-1
Extra Example 2: Area of Triangle Given Vertices
-2
Derivatives

1h 28m 27s

Intro
0:00
Definition and Geometric Interpretation
1:06
Example: F(x) is a Polynomial
1:14
Example: Parabola
2:48
F(x+h)
4:04
F(x+h)-F(x)/h
5:38
Slope of the Tangent
9:53
df/dx=f'
10:30
Derivatives of Power of x
13:11
F(x)=1 or Any Constant =0
13:27
F(x) =x = 1
15:13
F(x)= x2 = 2x
16:15
F(x)= x3 = 3x2
18:26
Derivatives of Sin(x), Cos(x) , Exp(x)
22:40
f(x)=Six x =cos(x)
22:51
Cos(x)=1 X= in Radians
27:50
Sin(x)=1 X= in Radians
28:55
e^x where x= in Radians
29:49
Derivative of u(x) v(x)
39:17
Derivative of Product of Two Functions f(x) =x^2 Sin(x)
39:30
Derivative of u(x)/v(x)
46:15
F(u/v)= f(u(x+h)/v(x+h)
46:23
Chain Rule
51:40
Example: F(x) =(x^2-1)^5
51:53
F(x)=Sin 3x
56:51
F(x) =e^-2x
58:21
Extra Example 1: Minima and Maxima
-1
Extra Example 2: Derivative
-2
Extra Example 3: Fermat's Principle to Derive Snell's Law
-3
Integrals

1h 13m 28s

Intro
0:00
Definite Integrals
0:20
F(x)
0:29
Area
10:43
Indefinite Integrals
13:53
Suppose Function f(y)=∫f(y) dy
15:07
g(x)=∫ f(x) dx
21:45
∫2 dx=2x+c
22:40
Evaluation of Definite Integrals
25:20
∫f(x') dx'=g(x)
25:35
Integral of Sin(x) ,Cos(x) , and Exp(x)
36:18
∫ sinx dx=-cos x+c
36:56
∫ cosx dx=sin x+c
39:32
∫ co2x dx=sin2x
40:09
∫Cosωdt=1/ωsin ωdt
42:42
∫e^x dx=e^x+c
43:32
Integration by Substitution
45:23
∫x(x^2 -1)dx
46:01
Integration by Parts
52:30
d/dx=(uv)'
52:45
∫udv=∫d(uv)-∫Vdu =uv-∫vdu
54:20
∫xe^x dx/dv
56:11
Extra Example 1: Integral
-1
Extra Example 2: Integral
-2
Motion in One Dimension

1h 19m 35s

Intro
0:00
Position, Distance, and Displacement
0:12
Position of the Object
0:30
Distance Traveled by The Object
5:34
Displacement of The Object
9:05
Average Speed Over a Certain Time Interval
14:46
Example Of an Object
15:15
Example: Calculating Average Speed
20:19
Average Velocity Over a Time Interval
22:22
Example Calculating Average Velocity of an Object
22:45
Instantaneous Velocity
30:45
Average Acceleration Over a Time Interval
40:50
Example: Average Acceleration of an Object
42:01
Instantaneous Acceleration
47:17
Example: Acceleration of Time T
47:33
Example with Realistic Equation
49:52
Motion With Constant Acceleration: Kinematics Equation
53:39
Example: Motion of an Object with Constant Acceleration
53:55
Extra Example 1: Uniformly Accelerated Motion
-1
Extra Example 2: Catching up with a Car
-2
Extra Example 3: Velocity and Acceleration
-3
Kinematics Equation From Calculus

47m 45s

Intro
0:00
Velocity and Acceleration
0:27
Particle moves In x Direction
0:35
Instantaneous Velocity for Δt =0
3:05
Acceleration (Change in Time) v(t+=Δt)-v(t) /Δt
4:58
Example
8:08
x(t) =(-4+3t+2t^2)
8:18
Finding Average velocity at 10sec
8:45
V at t=3s
10:28
x(t) =0 ,0.2 sin (2t)
12:20
Finding Velocity
12:50
Constant Acceleration
15:29
Object Moving with Constant Acceleration
15:40
Find Velocity and Position at Later Time t
18:23
v=∫a dt
19:50
V(t) =v0+at
23:33
v(t) =dx/dt x=∫vdt
24:14
T=v-v0/a
29:26
Extra Example 1: Velocity and Acceleration
-1
Extra Example 2: Particle Acceleration
-2
Freely Falling Objects

1h 28m 59s

Intro
0:00
Acceleration Due to Gravity
0:11
Dropping an Object at Certain Height
0:25
Signs : V , A , D
7:07
Example: Shooting an Object Upwards
7:34
Example: Ground To Ground
12:13
Velocity at Maximum Height
14:30
Time From Ground to Ground
23:10
Shortcut: Calculate Time Spent in Air
24:07
Example: Object Short Downwards
30:19
Object Short Downwards From a Height H
30:30
Use of Quadratic Formula
36:23
Example: Bouncing Ball
41:00
Ball Released From Certain Height
41:22
Time Until Stationary
43:10
Coefficient of Restitution
46:40
Example: Bouncing Ball. Continued
53:02
Extra Example 1: Object Shot Off Cliff
-1
Extra Example 2: Object Released Off Roof
-2
Extra Example 3: Rubber Ball (Coefficient of Restitution)
-3
Motion in Two Dimensions, Part 1

1h 8m 38s

Intro
0:00
Position, Displacement, Velocity, Acceleration
0:10
Position of an Object in X-Y Plane
0:19
Displacement of an Object
2:48
Average Velocity
4:30
Instantaneous Velocity at Time T
5:22
Acceleration of Object
8:49
Projectile Motion
9:57
Object Shooting at Angle
10:15
Object Falling Vertically
14:48
Velocity of an Object
18:17
Displacement of an Object
19:20
Initial Velocity Remains Constant
21:24
Deriving Equation of a Parabola
25:23
Example: Shooting a Soccer Ball
25:25
Time Ball Spent in Air (Ignoring Air Resistance)
27:48
Range of Projectile
34:49
Maximum Height Reached by the Projectile
36:25
Example: Shooting an Object Horizontally
40:38
Time Taken for Shooting
42:34
Range
46:01
Velocity Hitting Ground
46:30
Extra Example 1: Projectile Shot with an Angle
-1
Extra Example 2: What Angle
-2
Motion in Two Dimensions, Part 2: Circular Dimension

1h 1m 54s

Intro
0:00
Uniform Circular Motion
0:15
Object Moving in a Circle at Constant Speed
0:26
Calculation Acceleration
3:30
Change in Velocity
3:45
Magnitude of Acceleration
14:21
Centripetal Acceleration
18:15
Example: Earth Rotating Around The Sun
18:42
Center of the Earth
20:45
Distance Travelled in Making One Revolution
21:34
Acceleration of the Revolution
23:37
Tangential Acceleration and Radial Acceleration
25:35
If Magnitude and Direction Change During Travel
26:22
Tangential Acceleration
27:45
Example: Car on a Curved Road
29:50
Finding Total Acceleration at Time T if Car is at Rest
31:13
Extra Example 1: Centripetal Acceleration on Earth
-1
Extra Example 2: Pendulum Acceleration
-2
Extra Example 3: Radius of Curvature
-3
Newton's Laws of Motion

1h 29m 51s

Intro
0:00
Force
0:21
Contact Force (Push or Pull)
1:02
Field Forces
1:49
Gravity
2:06
Electromagnetic Force
2:43
Strong Force
4:12
Weak Force
5:17
Contact Force as Electromagnetic Force
6:08
Focus on Contact Force and Gravitational Force
6:50
Newton's First Law
7:37
Statement of First Law of Motion
7:50
Uniform Motion (Velocity is Constant)
9:38
Inertia
10:39
Newton's Second Law
11:19
Force as a Vector
11:35
Statement of Second Law of Motion
12:02
Force (Formula)
12:22
Example: 1 Force
13:04
Newton (Unit of Force)
13:31
Example: 2 Forces
14:09
Newton's Third Law
19:38
Action and Reaction Law
19:46
Statement of Third Law of Motion
19:58
Example: 2 Objects
20:15
Example: Objects in Contact
21:54
Example: Person on Earth
22:54
Gravitational Force and the Weight of an Object
24:01
Force of Attraction Formula
24:42
Point Mass and Spherical Objects
26:56
Example: Gravity on Earth
28:37
Example: 1 kg on Earth
35:31
Friction
37:09
Normal Force
37:14
Example: Small Force
40:01
Force of Static Friction
43:09
Maximum Force of Static Friction
46:03
Values of Coefficient of Static Friction
47:37
Coefficient of Kinetic Friction
47:53
Force of Kinetic Friction
48:27
Example: Horizontal Force
49:36
Example: Angled Force
52:36
Extra Example 1: Wire Tension
-1
Extra Example 2: Car Friction
-2
Extra Example 3: Big Block and Small Block
-3
Applications of Newton's Laws, Part 1: Inclines

1h 24m 35s

Intro
0:00
Acceleration on a Frictionless Incline
0:35
Force Action on the Object(mg)
1:31
Net Force Acting on the Object
2:20
Acceleration Perpendicular to Incline
8:45
Incline is Horizontal Surface
11:30
Example: Object on an Inclined Surface
13:40
Rough Inclines and Static Friction
20:23
Box Sitting on a Rough Incline
20:49
Maximum Values of Static Friction
25:20
Coefficient of Static Friction
27:53
Acceleration on a Rough Incline
29:00
Kinetic Friction on Rough Incline
29:15
Object Moving up the Incline
33:20
Net force on the Object
36:36
Example: Time to Reach the Bottom of an Incline
41:50
Displacement is 5m Down the Incline
45:26
Velocity of the Object Down the Incline
47:49
Extra Example 1: Bottom of Incline
-1
Extra Example 2: Incline with Initial Velocity
-2
Extra Example 3: Moving Down an Incline
-3
Applications of Newton's Laws, Part 2: Strings and Pulleys

1h 10m 3s

Intro
0:00
Atwood's Machine
0:19
Object Attached to a String
0:39
Tension on a String
2:15
Two Objects Attached to a String
2:23
Pulley Fixed to the Ceiling, With Mass M1 , M2
4:53
Applying Newton's 2nd Law to Calculate Acceleration on M1, M2
9:21
One Object on a Horizontal Surface: Frictionless Case
17:36
Connecting Two Unknowns, Tension and Acceleration
20:27
One Object on a Horizontal Surface: Friction Case
23:57
Two Objects Attached to a String with a Pulley
24:14
Applying Newton's 2nd Law
26:04
Tension of an Object Pulls to the Right
27:31
One of the Object is Incline : Frictionless Case
32:59
Sum of Two Forces on Mass M2
34:39
If M1g is Larger Than M2g
36:29
One of the Object is Incline : Friction Case
40:29
Coefficient of Kinetic Friction
41:18
Net Force Acting on M2
45:12
Extra Example 1: Two Masses on Two Strings
-1
Extra Example 2: Three Objects on Rough Surface
-2
Extra Example 3: Acceleration of a Block
-3
Accelerating Frames

1h 13m 28s

Intro
0:00
What Does a Scale Measure
0:11
Example: Elevator on a Scale
0:22
Normal Force
4:57
Apparent Weight in an Elevator
7:42
Example: Elevator Starts Moving Upwards
9:05
Net Force (Newton's Second Law)
11:34
Apparent Weight
14:36
Pendulum in an Accelerating Train
15:58
Example: Object Hanging on the Ceiling of a Train
16:15
Angle In terms of Increased Acceleration
22:04
Mass and Spring in an Accelerating Truck
23:40
Example: Spring on a Stationary Truck
23:55
Surface of Truck is Frictionless
27:38
Spring is Stretched by distance X
28:40
Cup of Coffee
29:55
Example: Moving Train and Stationary Objects inside Train
30:05
Train Moving With Acceleration A
32:45
Force of Static Friction Acting on Cup
36:30
Extra Example 1: Train Slows with Pendulum
-1
Extra Example 2: Person in Elevator Releases Object
-2
Extra Example 3: Hanging Object in Elevator
-3
Circular Motion, Part 1

1h 1m 15s

Intro
0:00
Object Attached to a String Moving in a Horizontal Circle
0:09
Net Force on Object (Newton's Second Law)
1:51
Force on an Object
3:03
Tension of a String
4:40
Conical Pendulum
5:40
Example: Object Attached to a String in a Horizontal Circle
5:50
Weight of an Object Vertically Down
8:05
Velocity And Acceleration in Vertical Direction
11:20
Net Force on an Object
13:02
Car on a Horizontal Road
16:09
Net Force on Car (Net Vertical Force)
18:03
Frictionless Road
18:43
Road with Friction
22:41
Maximum Speed of Car Without Skidding
26:05
Banked Road
28:13
Road Inclined at an Angle ø
28:32
Force on Car
29:50
Frictionless Road
30:45
Road with Friction
36:22
Extra Example 1: Object Attached to Rod with Two Strings
-1
Extra Example 2: Car on Banked Road
-2
Extra Example 3: Person Held Up in Spinning Cylinder
-3
Circular Motion, Part 2

50m 29s

Intro
0:00
Normal Force by a Pilot Seat
0:14
Example : Pilot Rotating in a Circle r and Speed s
0:33
Pilot at Vertical Position in a Circle of Radius R
4:18
Net Force on Pilot Towards Center (At Bottom)
5:53
Net Force on Pilot Towards Center (At Top)
7:55
Object Attached to a String in Vertical Motion
10:46
Example: Object in a Circle Attached to String
10:59
Case 1: Object with speed v and Object is at Bottom
11:30
Case 2: Object at Top in Vertical Motion
15:24
Object at Angle ø (General Position)
17:48
2 Radial Forces (Inward & Outward)
20:32
Tension of String
23:44
Extra Example 1: Pail of Water in Vertical Circle
-1
Extra Example 2: Roller Coaster Vertical Circle
-2
Extra Example 3: Bead in Frictionless Loop
-3
Work and Energy, Part 1

1h 24m 46s

Intro
0:00
Work in One Dimension: Constant Force
0:11
Particle Moving in X-Axis
0:24
Displacement Δx=x2-x1
1:35
Work Done by the Force W=FΔX
2:25
Example: Object Being Pushed for 10 m (Frictionless case)
3:31
Example: Elevator Descends with constant Velocity
5:37
Work by Tension
9:06
Work in One Dimension: Variable Force
11:28
Object Displaced from a to b Under Action of Force
12:06
Total Work= F(x1) Δx1
19:48
Special Case : F(x) =F
22:56
Work Done by a Spring
24:30
Spring Attached to a Object
24:42
Spring Stretched
25:40
Spring Compressed and Released
30:30
Hookes Law
32:05
W=∫F(x) dx ,Initial Position to Final Position
36:25
Work in Three Dimension: Constant Force
41:54
3 Components Of 3 Dimensions
45:45
Work Done By F=F.Δx
47:30
Example
48:58
Object Moves Up and Inclined
49:10
Work Done by Gravity=F.Δr
49:50
W=F.Δr= -mgz
53:50
Work Done By Normal Force=0
54:33
Work in Three Dimension: Variable Force
55:45
Object Moving From A to B with Time
56:03
W=∫f.dr
57:45
Extra Example 1: Work Done By Force
-1
Extra Example 2: Mass on Half Ring
-2
Extra Example 3: Force with Two Paths
-3
Work and Energy, Part 2

1h 12m 53s

Intro
0:00
Work Kinetic Energy Theorem
0:16
Object Moves in 3 Dimensions
1:51
Work Done by Net Force =W=∫f.dr
3:27
W=Change in Kinetic Energy
15:11
Example
16:00
Object Moving on Surface with Mass 10 N
16:12
Using Newton's Second Law
18:26
Using Work Kinetic Energy Theorem
21:32
Gravitational Potential Energy
24:30
Example of a Particle in 3 Dimensions
24:47
Work Done By Force of Gravity
26:09
Conservation of Energy
36:37
Object in a Projectile
36:48
Work Done by Gravity
39:50
Example
43:45
Frictionless Track
44:20
Example
50:49
Pendulum: Object Attached to a String at Height H
51:07
Finding Tension in a String
52:20
Extra Example 1: Object Pulled by Angled Force
-1
Extra Example 2: Projectile Shot at Angle
-2
Conservation of Energy, Part 1

1h 32m 50s

Intro
0:00
Conservative Forces
0:10
Given a Force
4:01
Consider a Particle Moves from P1 to P2 on Path
5:40
Work Done by Force
8:28
Example
14:56
Gravity
15:20
Spring with Block Moves and Stretched
17:36
Friction is Net Conservative
23:29
Path 1 Straight
27:04
Along Path 2
30:07
Potential Energy by a Conservative Force
33:23
Choose Reference Point (Potential Energy =0)
33:51
Define Potential Energy at Point P
35:23
Conservation of Energy
40:58
Object Moving from P1 -P2
41:50
Work Kinetic Energy Theorem
41:58
Potential Energy of a Spring
48:42
Spring Stretched with Mass M, Find Potential Energy
49:13
Example
53:45
Force Acting on Particle in One Dimension
54:10
Extra Example 1: Work Done By Gravity
-1
Extra Example 2: Prove Constant Force is Conservative
-2
Extra Example 3: Work Done by Force
-3
Extra Example 4: Compression of Spring
-4
Conservation of Energy, Part 2

1h 7m 48s

Intro
0:00
In Presence of Friction
0:13
Work Energy Theorem
3:05
Work Done BY Friction is Negative
6:51
Example
10:12
Object on Inclined Surface with Friction
10:20
Heat, Magnitude by Friction
12:42
Work Done By Friction
13:01
Calculation of the Force From The Potential Energy
19:15
Defining Potential Energy with Conservation of Energy
19:35
Potential Energy and Equilibrium
31:16
Spring Stretched with Mass M
31:28
Stable Equilibrium
35:52
Unstable Equilibrium
40:50
Example
41:02
Two Objects or Two Atoms
41:12
Leonard John's Potential
42:15
Power
47:38
Rate at Force Work Done
47:54
Average Power
49:01
Instant Power Delivered at Time t
49:20
Horse Power
53:10
Extra Example 1: Force from Potential Energy
-1
Extra Example 2: Mass with Two Springs
-2
Extra Example 3: Block Pulled with Friction
-3
Conservation of Energy, Part 3 (Examples)

1h 11m 58s

Intro
0:00
Spring Loaded Gun
0:26
Spring with Bullet
0:43
Finding the Force Constant if Mass of Bullet is Given
2:48
Compression of a Spring
5:10
Sliding Object
11:33
Object Sliding on a Frictionless Surface
12:15
Spring at the End of a Slide
12:46
Using Conservation of Energy K1+u1=K2+U2
15:06
Finding Velocity and Energy
17:36
Block Spring System with Friction
33:05
Spring is Unstretched at Equilibrium
33:35
Spring is Compressed
33:57
Finding Total Energy
39:02
Losing Contact on a Circular Track
46:16
Objects Slides on a Circular Track
47:25
Normal Force=0
48:10
Centripetal Force
48:57
Finding Velocity at Given Angle
49:25
Energy at the Top
50:55
Contact Lost
54:55
Horse Pulling a Carriage
56:07
Horse Power
56:40
Power=FV
57:11
Extra Example 1: Elevator with Friction
-1
Extra Example 2: Loop the Loop
-2
Collisions, Part 1

1h 31m 19s

Intro
0:00
Linear Momentum
0:10
Example: Object of Mass m with Velocity v
0:25
Example: Object Bounced on a Wall
1:08
Momentum of Object Hitting a Wall
2:20
Change in Momentum
4:10
Force is the Rate of Change of Momentum
4:30
Force=Mass*Acceleration (Newton's Second Law)
4:45
Impulse
10:24
Example: Baseball Hitting a Bat
10:40
Force Applied for a Certain Time
11:50
Magnitude Plot of Force vs Time
13:35
Time of Contact of Baseball = 2 milliseconds (Average Force by Bat)
17:42
Collision Between Two Particles
22:40
Two Objects Collide at Time T
23:00
Both Object Exerts Force on Each Other (Newton's Third Law)
24:28
Collision Time
25:42
Total Momentum Before Collision = Total momentums After Collision
32:52
Collision
33:58
Types of Collisions
34:13
Elastic Collision ( Mechanical Energy is Conserved)
34:38
Collision of Particles in Atoms
35:50
Collision Between Billiard Balls
36:54
Inelastic Collision (Rubber Ball)
39:40
Two Objects Collide and Stick (Completely Inelastic)
40:35
Completely Inelastic Collision
41:07
Example: Two Objects Colliding
41:23
Velocity After Collision
42:14
Heat Produced=Initial K.E-Final K.E
47:13
Ballistic Pendulum
47:37
Example: Determine the Speed of a Bullet
47:50
Mass Swings with Bulled Embedded
49:20
Kinetic Energy of Block with the Bullet
50:28
Extra Example 1: Ball Strikes a Wall
-1
Extra Example 2: Clay Hits Block
-2
Extra Example 3: Bullet Hits Block
-3
Extra Example 4: Child Runs onto Sled
-4
Collisions, Part 2

1h 18m 48s

Intro
0:00
Elastic Collision: One Object Stationary
0:28
Example: Stationary Object and Moving Object
0:42
Conservation of Momentum
2:48
Mechanical Energy Conservation
3:43
Elastic Collision: Both Objects Moving
17:34
Example: Both Objects Moving Towards Each Other
17:48
Kinetic Energy Conservation
19:20
Collision With a Spring-Block System
29:17
Example: Object of Mass Moving with Velocity
29:30
Object Attached to Spring of Mass with Velocity
29:50
Two Objects Attached to a Spring
31:30
Compression of Spring after Collision
33:41
Before Collision: Total Energy (Conservation of Energy)
37:25
After Collision: Total Energy
38:49
Collision in Two Dimensions
42:29
Object Stationary and Other Object is Moving
42:46
Head on Collision (In 1 Dimension)
44:07
Momentum Before Collision
45:45
Momentum After Collision
46:06
If Collision is Elastic (Conservation of Kinetic Energy) Before Collision
50:29
Example
51:58
Objects Moving in Two Directions
52:33
Objects Collide and Stick Together (Inelastic Collision)
53:28
Conservation of Momentum
54:17
Momentum in X-Direction
54:27
Momentum in Y-Direction
56:15
Maximum Height after Collision
-1
Extra Example 2: Two Objects Hitting a Spring
-2
Extra Example 3: Mass Hits and Sticks
-3
Center of Mass, Part 1

1h 33m 46s

Collection of Particles
0:13
System of Coordinates
0:40
Coordinates of Center of Mass
2:25
Four Particles
10:10
Center of Mass at Xcm
13:20
Center of Mass at Ycm
15:07
Extended Objects
17:00
Consider a Object
17:30
Dividing Object in to Smaller Particles
19:07
Divide the Volume N into Pieces
23:10
Center of Mass of a Rod
31:02
Total Mass of Rod
35:30
Center of Mass of a Right Angle
42:27
Right Triangle Placed in Coordinates
42:40
Tiny Strip on a Triangle
45:05
Intersection of a Point
56:19
Extra Example 1: Center of Mass Two Objects
-1
Extra Example 2: Bent Rod Center of Mass
-2
Extra Example 3: Triangle Center of Mass
-3
Center of Mass, Part 2

1h 19m 15s

Intro
0:00
Motion of a System of Particles
0:53
Position Vector of Center of Mass
2:30
Total Momentum
7:08
Net Force Acting on a Particle
9:32
Exploding a Projectile
19:12
Shooting a Projectile in x-z Plane
19:50
Projectile Explodes into 2 pieces of Equal Mass
27:19
Rocket Propulsion
35:09
Rocket with Mass m and Velocity v
35:25
Rocket in Space
53:39
Rocket in Space with Speed=3000m/s
53:48
Engine is Turned On
54:19
Final Mass=1/2 Initial Mass
57:15
Speed after Fuel is Burned
58:09
Extra Example 1: Ball Inelastic Hits Other Ball
-1
Extra Example 2: Rocket Launch Thrust
-2
Rotation of a Rigid Body About a Fixed Axis

1h 13m 20s

Intro
0:00
Particle in Circular Motion
0:11
Specify a Position of a Particle
0:55
Radian
3:02
Angular Displacement
8:50
Rotation of a Rigid Body
15:36
Example: Rotating Disc
16:17
Disk at 5 Revolution/Sec
17:24
Different Points on a Disk Have Different Speeds
21:56
Angular Velocity
23:03
Constant Angular Acceleration: Kinematics
31:11
Rotating Disc
31:42
Object Moving Along x-Axis (Linear Case)
33:05
If Alpha= Constant
35:15
Rotational Kinetic Energy
42:11
Rod in X-Y Plane, Fixed at Center
42:43
Kinetic Energy
46:45
Moment of Inertia
52:46
Moment of Inertia for Certain Shapes
54:06
Rod at Center
54:47
Ring
55:45
Disc
56:35
Cylinder
56:56
Sphere
57:20
Extra Example 1: Rotating Wheel
-1
Extra Example 2: Two Spheres Attached to Rotating Rod
-2
Moment of Inertia

1h 32m 22s

Intro
0:00
Review of Kinematic Rotational Equation
0:12
Rigid Body Rotation on a Axis
0:29
Constant Angular Acceleration
10:17
Rotational Kinetic Energy
16:33
Particle Moving in a Circle
16:42
Moment of Inertia
22:43
Moment of Inertia of a Uniform Rod
25:10
Dividing the Body in Many Pieces
27:40
Total Mass=M Lamda=m/l
29:21
Axis Through the Center of Mass
34:02
Uniform Solid Cylinder
35:13
Cylinder of Length L
35:25
Finding Moment of Inertia I=∫r2 dm
36:04
Volume of Cylinder
40:02
Other Shapes
44:37
Ring
45:08
Disc
45:22
Sphere
45:50
Spherical Shell
45:49
Parallel Axis Theorem
46:46
Object with Center of Mass
47:12
Consider Another Axis Parallel to Primary Axis
47:35
Extra Example 1: Moment of Inertia for Ring and Disk
-1
Extra Example 2: Moment of Inertia for Sphere
-2
Extra Example 3: Moment of Inertia for Spherical Shell
-3
Angular Momentum

1h 3m 48s

Intro
0:00
Angular Momentum of Particle
0:06
Magnitude of Angular Momentum
2:27
Right Hand Rule
3:00
Particle Moving in Circular Motions
4:18
Angular Momentum of a Rigid Body
6:44
Consider a Rigid Body
7:06
Z Axis Through Center
7:27
Rotate About the Z-Axis
18:57
Example
19:36
Rotating in Circular Motion
20:08
Consider a Mass on the Rigid Body
20:38
Angular Momentum of Disk
26:14
Rotation About an Axis of Symmetry
26:27
Perpendicular to Symmetry
27:35
Cylinder
29:02
Sphere
29:23
Rotating on Axis
29:40
Rigid Body Rotates About Axis of Symmetry
40:33
The Z-Component of Angular Momentum
40:56
Consider any Dmi on The Surface
41:57
Example
49:40
Cylinder
49:55
Extra Example 1: Rod Angular Momentum
-1
Extra Example 2: Particle Angular Momentum
-2
Rotational Dynamics

1h 19m 59s

Intro
0:00
Torque
0:10
Object Fixed at Center
1:34
τ=r Fsin θ
11:14
Relation of Torque to Angular Momentum
11:47
Derivative of Momentum
12:34
Consider a Particle With Velocity =V
13:51
For a Rigid Body
16:45
Equation of Rotational Motion
25:23
Object Rigid Body Rotating on Axis
27:14
Torque Acting on the Object
27:36
Torque About Axis of Rotation
30:55
Block and a Pulley
31:55
Rope with Mass=m and Radius of Pulley
32:40
Finding Acceleration and Tension
37:26
Atwood's Machine
41:57
Pulley with Masses m1, m2 and Radius R
42:49
Acceleration
50:15
Extra Example 1: Uniform Rod
-1
Extra Example 2: Two Blocks with Strings
-2
Extra Example 3: Thin Disk
-3
Energy Consideration by Rotational Motion

1h 10m 28s

Intro
0:00
Work Done By Torque
0:15
Rigid Body Rotating about Z-axis
1:33
Rigid Body Rotating about Z-axis
3:01
Point p Rotates on Circle and Perpendicular to z
4:19
Work Kinetic Energy Theorem for Rotational Motion
15:36
Work Done By Torque
16:43
Work Done By Net Torque=Kf-Ki
20:31
Conservation of Mechanical Energy in Rotational Motion
21:41
Conservation Force Acting
22:40
Work Done by Gravity
23:15
Work Done by Torque
25:38
Power Delivered by Torque
27:12
Power by Force
27:58
Rotating Rod
30:03
Rod Clamped at One End
30:35
Angular Speed
30:50
Moment of Inertia About Axis of Rotation
35:15
Speed of Free End
37:40
Another Rotating Rod
37:59
Rod Standing on Surface
38:37
End Does Not Slip
39:01
Speed of Free End
41:20
Strikes Ground
42:13
Extra Example 1: Peg and String
-1
Extra Example 2: Solid Disk
-2
Extra Example 3: Rod and Sphere
-3
Conservation of Angular Momentum

1h 6m 57s

Intro
0:00
Conservation of Angular Momentum in an Isolated System
0:13
Linear Case
0:45
Torque=Rate if Changed in Angular Momentum
1:29
Isolated System
1:59
Neutron Star
4:13
Star Rotates About Some Axis
4:31
Merry Go Round
12:50
Consider a Large Disc
13:06
Total Angular Momentum Calculated
18:59
Sticky Clay Sticking a Rod
19:07
Rod of Length L With Pivot at End
19:37
Piece of Clay of Mass m and Velocity v
19:45
Angular Momentum Calculated
28:58
Extra Example 1: Rod with Beads
-1
Extra Example 2: Mass Striking Rod
-2
Extra Example 3: Wood Block and Bullet
-3
Rolling Motion

1h 36m 9s

Intro
0:00
Pure Rolling Motion
0:10
Disc Rolling on a Surface R (Rolling Without Sipping)
0:50
When Disc Rotates, Center of Mass Moves
5:48
Acceleration of Center of Mass
8:43
Kinetic Energy
11:03
Object in Pure Rotation
11:16
Pure Translation
13:28
Rotation and Translation
15:24
Cylinder Rolling Down an Incline
23:55
Incline
24:15
Cylinder Starts From Rest
24:44
Which Moves Faster
37:02
Rolling a Ring, Disc, Sphere
37:19
Ring I=Mr2
41:30
Disc I= 1/2 Mr2
42:31
Sphere I= 2/5 mr2
43:21
Which Goes Faster
49:15
Incline with a Object Towards the Inclination
49:30
Extra Example 1: Rolling Cylinder
-1
Extra Example 2: Nonuniform Cylinder
-2
Extra Example 3: String Around Disk
-3
Universal Gravitation

1h 9m 20s

Intro
0:00
Newton's Law of Gravity
0:09
Two Particles of Mass m1,m2
1:22
Force of Attraction
3:02
Sphere and Small Particle of Mass m
4:39
Two Spheres
5:35
Variation of g With Altitude
7:24
Consider Earth as an Object
7:33
Force Applied To Object
9:27
At or Near Surface of Earth
11:51
Satellites
15:39
Earth and Satellite
15:45
Geosynchronous Satellite
21:25
Gravitational Potential Energy
27:32
Object and Earth Potential Energy=mgh
24:45
P.E=0 When Objects are Infinitely Separated
30:32
Total Energy
38:28
If Object is Very Far From Earth, R=Infinity
40:25
Escape
42:33
Shoot an Object Which Should Not Come Back Down
43:06
Conservation of Energy
48:48
Object at Maximum Height (K.E=0)
45:22
Escape Velocity (Rmax = Infinity)
46:50
Extra Example 1: Density of Earth and Moon
-1
Extra Example 2: Satellite Orbiting Earth
-2
Kepler's Laws

1h 12m 25s

Intro
0:00
Kepler's First law
2:18
Any Point on Ellipse
4:33
Semi Major Axis
6:35
Semi Minor Axis
7:05
Equation of Ellipse
7:32
Eccentricity
16:05
Kepler's Second Law
19:46
Radius Vector
20:31
Torque by Force of Gravity
25:00
Kepler's Third Law
36:49
Time Take for the Planet to make 1 Revolution
37:20
Period
41:26
Mass of Sun
43:39
Orbit of Earth is Almost Circle
45:11
Extra Example 1: Halley's Comet
-1
Extra Example 2: Two Planets Around Star
-2
Extra Example 3: Neutron Star
-3
Energy and Gravitation

35m 4s

Intro
0:00
Gravitational Potential Energy
0:10
Conservative Force
1:45
Along Path A ∫f.dr=0
7:35
Along Path B ∫f.dr=-1
10:30
Δu= ∫f r1 to r2
10:58
Near the Surface of the Earth
17:07
Two Points on Surface of Earth
17:22
Planets and Satellites
24:40
Circular Orbits
24:59
Elliptical Orbits
30:54
Static Equilibrium

1h 38m 57s

Intro
0:00
Torque
0:09
Introduction to Torque
0:16
Rod in X-Y Direction
0:30
Particle in Equilibrium
18:15
Particle in Equilibrium, Net Force=0
18:30
Extended Object Like a Rod
19:13
Conditions of Equilibrium
26:34
Forces Acting on Object (Proof of Torque)
31:46
The Lever
35:38
Rod on Lever with Two Masses
35:51
Standing on a Supported Beam
40:53
Example : Wall and Beam Rope Connect Beam and Wall
41:00
Net Force
45:38
Net Torque
48:33
Finding ø
52:50
Ladder About to Slip
53:38
Example: Finding Angle ø Where Ladder Doesn't slip
53:44
Extra Example 1: Bear Retrieving Basket
-1
Extra Example 2: Sliding Cabinet
-2
Simple Harmonic System Spring Block System

1h 2m 35s

Intro
0:00
Restoring Force
0:41
Spring Attached to a Block
0:53
Spring Stretched
1:58
Force=Kx (K=Force Constant)
5:45
Simple Harmonic Motion
11:31
According to Newton's Law F=mxa
11:55
Equation of Motion
15:15
Frequency, Period, Velocity, and Acceleration
34:23
Object Without Stretching
34:52
Object Stretched
35:15
Acceleration a=dv/dt
43:20
Block Spring System
53:01
Object Being Compressed
53:26
Energy Consideration
57:47
Example
59:48
Spring Being Compressed
59:55
The Pendulum

1h 1m 55s

Intro
0:00
Simple Pendulum
0:07
Mass Attached to the String
0:25
Torque=mgr Perpendicular
7:34
Moment of Inertia
15:36
When φ<<1
24:30
Example
33:13
Mass Hanging with 1kg and Length 1 M and Velocity 2m
33:26
Period
34:50
Frequency
35:40
Ki+ui=Kf+uf
37:01
Physical Pendulum
41:39
Rigid Body with a Pivot and let it Oscillate
42:00
Torque Produced
47:58
Example
53:35
Rod Fixed and Made to Oscillated
53:40
Period
54:40
Torsional Pendulum
57:57
Mass Suspended with a Torsional Fiber
58:15
Torque Produced
58:55
Example
1:00:05
Wire With Torsional -K
1:00:11
Damped and Forced Oscillation

53m 35s

Intro
0:00
Damped Oscillation
0:11
Spring Oscillation
0:45
Force of Friction F=-bv
5:20
Spring in Absence of Friction
6:10
No Damping
8:29
In Presence of Damping
8:41
Example
21:07
Pendulum Oscillating at 10 Degrees
21:23
After 10 Min Amplitude Becomes 5 Degrees
22:10
Forced Oscillation
30:18
Spring Oscillating up and Down, Applying Force
35:25
Steady State Solution
41:49
Example
46:48
Spring with Object Mass=0.1 kg
47:05
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