I. Mechanics 

Introduction to Physics (Basic Math) 
1:17:37 
 
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 (306090) 
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 
2:47  
 
Extra Example 2: Law of Cosines 
12:52  
 
Extra Example 3: Dimensional Analysis 
11:43  

Vector Addition 
1:10:31 
 
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 
9:57  
 
Extra Example 2: Angle Between Vectors 
4:10  
 
Extra Example 3: Vector Addition 
4:51  

Dot Product and Cross Product 
1:06:17 
 
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 
2:46  
 
Extra Example 2: Area of Triangle Given Vertices 
8:29  

Derivatives 
1:28:27 
 
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^21)^5 
51:53  
 
 F(x)=Sin 3x 
56:51  
 
 F(x) =e^2x 
58:21  
 
Extra Example 1: Minima and Maxima 
7:00  
 
Extra Example 2: Derivative 
5:29  
 
Extra Example 3: Fermat's Principle to Derive Snell's Law 
16:33  

Integrals 
1:13:28 
 
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 
6:26  
 
Extra Example 2: Integral 
7:40  

Motion in One Dimension 
1:19:35 
 
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 
6:14  
 
Extra Example 2: Catching up with a Car 
8:33  
 
Extra Example 3: Velocity and Acceleration 
6:41  

Kinematics Equation From Calculus 
47:45 
 
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=vv0/a 
29:26  
 
Extra Example 1: Velocity and Acceleration 
8:25  
 
Extra Example 2: Particle Acceleration 
5:49  

Freely Falling Objects 
1:28:59 
 
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 
13:30  
 
Extra Example 2: Object Released Off Roof 
7:13  
 
Extra Example 3: Rubber Ball (Coefficient of Restitution) 
13:50  

Motion in Two Dimensions, Part 1 
1:08:38 
 
Intro 
0:00  
 
 Position, Displacement, Velocity, Acceleration 
0:10  
 
 Position of an Object in XY 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 
12:37  
 
Extra Example 2: What Angle 
6:55  

Motion in Two Dimensions, Part 2: Circular Dimension 
1:01:54 
 
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 
8:11  
 
Extra Example 2: Pendulum Acceleration 
7:12  
 
Extra Example 3: Radius of Curvature 
9:08  

Newton's Laws of Motion 
1:29:51 
 
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 
10:37  
 
Extra Example 2: Car Friction 
11:43  
 
Extra Example 3: Big Block and Small Block 
9:17  

Applications of Newton's Laws, Part 1: Inclines 
1:24:35 
 
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 
12:23  
 
Extra Example 2: Incline with Initial Velocity 
15:31  
 
Extra Example 3: Moving Down an Incline 
8:09  

Applications of Newton's Laws, Part 2: Strings and Pulleys 
1:10:03 
 
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 
5:28  
 
Extra Example 2: Three Objects on Rough Surface 
7:11  
 
Extra Example 3: Acceleration of a Block 
8:52  

Accelerating Frames 
1:13:28 
 
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 
11:54  
 
Extra Example 2: Person in Elevator Releases Object 
13:06  
 
Extra Example 3: Hanging Object in Elevator 
10:26  

Circular Motion, Part 1 
1:01:15 
 
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 
11:27  
 
Extra Example 2: Car on Banked Road 
9:29  
 
Extra Example 3: Person Held Up in Spinning Cylinder 
3:05  

Circular Motion, Part 2 
50:29 
 
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 
5:16  
 
Extra Example 2: Roller Coaster Vertical Circle 
3:57  
 
Extra Example 3: Bead in Frictionless Loop 
16:56  

Work and Energy, Part 1 
1:24:46 
 
Intro 
0:00  
 
Work in One Dimension: Constant Force 
0:11  
 
 Particle Moving in XAxis 
0:24  
 
 Displacement Δx=x2x1 
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 
3:19  
 
Extra Example 2: Mass on Half Ring 
12:07  
 
Extra Example 3: Force with Two Paths 
9:03  

Work and Energy, Part 2 
1:12:53 
 
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 
8:13  
 
Extra Example 2: Projectile Shot at Angle 
6:30  

Conservation of Energy, Part 1 
1:32:50 
 
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 
8:14  
 
Extra Example 2: Prove Constant Force is Conservative 
4:03  
 
Extra Example 3: Work Done by Force 
13:07  
 
Extra Example 4: Compression of Spring 
8:18  

Conservation of Energy, Part 2 
1:07:48 
 
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 
3:36  
 
Extra Example 2: Mass with Two Springs 
4:17  
 
Extra Example 3: Block Pulled with Friction 
6:04  

Conservation of Energy, Part 3 (Examples) 
1:11:58 
 
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 
7:02  
 
Extra Example 2: Loop the Loop 
5:34  

Collisions, Part 1 
1:31:19 
 
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.EFinal 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 
10:41  
 
Extra Example 2: Clay Hits Block 
8:35  
 
Extra Example 3: Bullet Hits Block 
11:37  
 
Extra Example 4: Child Runs onto Sled 
7:24  

Collisions, Part 2 
1:18:48 
 
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 SpringBlock 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 XDirection 
54:27  
 
 Momentum in YDirection 
56:15  
 
Maximum Height after Collision 
10:34  
 
Extra Example 2: Two Objects Hitting a Spring 
7:05  
 
Extra Example 3: Mass Hits and Sticks 
2:58  

Center of Mass, Part 1 
1:33:46 
 
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 
12:56  
 
Extra Example 2: Bent Rod Center of Mass 
15:17  
 
Extra Example 3: Triangle Center of Mass 
7:50  

Center of Mass, Part 2 
1:19:15 
 
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 xz 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 
12:35  
 
Extra Example 2: Rocket Launch Thrust 
6:47  

Rotation of a Rigid Body About a Fixed Axis 
1:13:20 
 
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 xAxis (Linear Case) 
33:05  
 
 If Alpha= Constant 
35:15  
 
Rotational Kinetic Energy 
42:11  
 
 Rod in XY 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 
6:44  
 
Extra Example 2: Two Spheres Attached to Rotating Rod 
8:45  

Moment of Inertia 
1:32:22 
 
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 
10:39  
 
Extra Example 2: Moment of Inertia for Sphere 
12:56  
 
Extra Example 3: Moment of Inertia for Spherical Shell 
11:41  

Angular Momentum 
1:03:48 
 
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 ZAxis 
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 ZComponent 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 
5:46  
 
Extra Example 2: Particle Angular Momentum 
4:20  

Rotational Dynamics 
1:19:59 
 
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 
8:49  
 
Extra Example 2: Two Blocks with Strings 
12:40  
 
Extra Example 3: Thin Disk 
7:00  

Energy Consideration by Rotational Motion 
1:10:28 
 
Intro 
0:00  
 
Work Done By Torque 
0:15  
 
 Rigid Body Rotating about Zaxis 
1:33  
 
 Rigid Body Rotating about Zaxis 
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=KfKi 
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 
5:51  
 
Extra Example 2: Solid Disk 
9:50  
 
Extra Example 3: Rod and Sphere 
12:03  

Conservation of Angular Momentum 
1:06:57 
 
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 
8:38  
 
Extra Example 2: Mass Striking Rod 
8:42  
 
Extra Example 3: Wood Block and Bullet 
20:32  

Rolling Motion 
1:36:09 
 
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 
15:16  
 
Extra Example 2: Nonuniform Cylinder 
7:55  
 
Extra Example 3: String Around Disk 
15:05  

Universal Gravitation 
1:09:20 
 
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 
7:09  
 
Extra Example 2: Satellite Orbiting Earth 
11:54  

Kepler's Laws 
1:12:25 
 
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 
11:18  
 
Extra Example 2: Two Planets Around Star 
6:27  
 
Extra Example 3: Neutron Star 
3:34  

Energy and Gravitation 
35:04 
 
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 
1:38:57 
 
Intro 
0:00  
 
Torque 
0:09  
 
 Introduction to Torque 
0:16  
 
 Rod in XY 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 
19:42  
 
Extra Example 2: Sliding Cabinet 
20:09  

Simple Harmonic System Spring Block System 
1:02:35 
 
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 
1:01:55 
 
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 
60:05  
 
 Wire With Torsional K 
60:11  

Damped and Forced Oscillation 
53:35 
 
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  