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Lecture Comments (2)

1 answer

Last reply by: Lukasz Skora
Wed Jan 18, 2012 9:41 AM

Post by Romin Abdolahzadi on December 7, 2010

[AT 48:37] If you do the integral of x^3 - the integral of x separately then you obtain a result of:

(x^4/4 - x^2/2) + c

Professor Jishi, through u-substitution, obtained a result of:

(x^2-1)^2/4 + c

Clearly we can see if we sub in a value of x=1 then we get completely different results; first one being -1/4 + C and second one giving 0 + C. Did Professor Jishi make a mistake? I keep looking at his u-substitution and it seems he does everything logically step-by-step.

Integrals

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
  • Definite Integrals 0:20
    • F(x)
    • Area
  • Indefinite Integrals 13:53
    • Suppose Function f(y)=∫f(y) dy
    • g(x)=∫ f(x) dx
    • ∫2 dx=2x+c
  • Evaluation of Definite Integrals 25:20
    • ∫f(x') dx'=g(x)
  • Integral of Sin(x) ,Cos(x) , and Exp(x) 36:18
    • ∫ sinx dx=-cos x+c
    • ∫ cosx dx=sin x+c
    • ∫ co2x dx=sin2x
    • ∫Cosωdt=1/ωsin ωdt
    • ∫e^x dx=e^x+c
  • Integration by Substitution 45:23
    • ∫x(x^2 -1)dx
  • Integration by Parts 52:30
    • d/dx=(uv)'
    • ∫udv=∫d(uv)-∫Vdu =uv-∫vdu
    • ∫xe^x dx/dv
  • Extra Example 1: Integral
  • Extra Example 2: Integral
Professor Jishi

Professor Jishi

Integrals

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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