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Dot Product and Cross Product

I. Mechanics: Lecture 3 | 66:17 min

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Post by Justin Malaer on January 20 at 01:57:08 PM

vector A cross vector A = zero? or does it equal the zero vector? Because at the beginning you said that a vector cross a vector gives you another vector. and zero is a scalar.

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Last reply by: Vineet Kumar
Wed Jun 12, 2013 12:10 AM

Post by Vineet Kumar on June 12 at 12:10:03 AM

I believe you messed up with the arithmethic at 21:33 i think it should be sqrt of 21 not 9

Dot Product and Cross Product

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AP Physics C: Mechanics

I. Mechanics
	Introduction to Physics (Basic Math)			77:37
		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 (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		2:47
		Extra Example 2: Law of Cosines		12:52
		Extra Example 3: Dimensional Analysis		11:43
	Vector Addition			70:31
		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			66:17
		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			88:27
		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^2-1)^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			73:28
		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			79:35
		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=v-v0/a	29:26
		Extra Example 1: Velocity and Acceleration		8:25
		Extra Example 2: Particle Acceleration		5:49
	Freely Falling Objects			88:59
		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			68:38
		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		12:37
		Extra Example 2: What Angle		6:55
	Motion in Two Dimensions, Part 2: Circular Dimension			61:54
		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			89:51
		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			84:35
		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			70:03
		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			73:28
		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			61:15
		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			84:46
		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		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			72:53
		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			92:50
		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			67:48
		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)			71:58
		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			91:19
		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.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		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			78:48
		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 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		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			93:46
		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			79:15
		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 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		12:35
		Extra Example 2: Rocket Launch Thrust		6:47
	Rotation of a Rigid Body About a Fixed Axis			73:20
		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 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		6:44
		Extra Example 2: Two Spheres Attached to Rotating Rod		8:45
	Moment of Inertia			92:22
		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			63:48
		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 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		5:46
		Extra Example 2: Particle Angular Momentum		4:20
	Rotational Dynamics			79:59
		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			70:28
		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		5:51
		Extra Example 2: Solid Disk		9:50
		Extra Example 3: Rod and Sphere		12:03
	Conservation of Angular Momentum			66:57
		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			96:09
		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			69:20
		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			72:25
		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			98:57
		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		19:42
		Extra Example 2: Sliding Cabinet		20:09
	Simple Harmonic System Spring Block System			62:35
		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			61:55
		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

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