  Dan Fullerton

Newton's Second & Third Laws of Motion

Slide Duration:

Section 1: Introduction
What is Physics?

7m 12s

Intro
0:00
Objectives
0:11
What is Physics?
0:27
Why?
0:50
0:51
Matter
1:27
Matter
1:28
Mass
1:43
Inertial Mass
1:50
Gravitational Mass
2:13
A Spacecraft's Mass
3:03
What is the Mass of the Spacecraft?
3:05
Energy
3:37
Energy
3:38
Work
3:45
Putting Energy and Work Together
3:50
Mass-Energy Equivalence
4:15
Relationship between Mass & Energy: E = mc²
4:16
Source of Energy on Earth
4:47
The Study of Everything
5:00
Physics is the Study of Everything
5:01
Mechanics
5:29
Topics Covered
5:30
Topics Not Covered
6:07
Next Steps
6:44
Three Things You'd Like to Learn About in Physics
6:45
Math Review

1h 51s

Intro
0:00
Objectives
0:10
Vectors and Scalars
1:06
Scalars
1:07
Vectors
1:27
Vector Representations
2:00
Vector Representations
2:01
2:54
2:55
Graphical Vector Subtraction
5:36
Graphical Vector Subtraction
5:37
Vector Components
7:12
Vector Components
7:13
Angle of a Vector
8:56
tan θ
9:04
sin θ
9:25
cos θ
9:46
Vector Notation
10:10
Vector Notation 1
10:11
Vector Notation 2
12:59
Example I: Magnitude of the Horizontal & Vertical Component
16:08
Example II: Magnitude of the Plane's Eastward Velocity
17:59
Example III: Magnitude of Displacement
19:33
Example IV: Total Displacement from Starting Position
21:51
Example V: Find the Angle Theta Depicted by the Diagram
26:35
Vector Notation, cont.
27:07
Unit Vector Notation
27:08
Vector Component Notation
27:25
Vector Multiplication
28:39
Dot Product
28:40
Cross Product
28:54
Dot Product
29:03
Dot Product
29:04
Defining the Dot Product
29:26
Defining the Dot Product
29:27
Calculating the Dot Product
29:42
Unit Vector Notation
29:43
Vector Component Notation
30:58
Example VI: Calculating a Dot Product
31:45
Example VI: Part 1 - Find the Dot Product of the Following Vectors
31:46
Example VI: Part 2 - What is the Angle Between A and B?
32:20
Special Dot Products
33:52
Dot Product of Perpendicular Vectors
33:53
Dot Product of Parallel Vectors
34:03
Dot Product Properties
34:51
Commutative
34:52
Associative
35:05
Derivative of A * B
35:24
Example VII: Perpendicular Vectors
35:47
Cross Product
36:42
Cross Product of Two Vectors
36:43
Direction Using the Right-hand Rule
37:32
Cross Product of Parallel Vectors
38:04
Defining the Cross Product
38:13
Defining the Cross Product
38:14
Calculating the Cross Product Unit Vector Notation
38:41
Calculating the Cross Product Unit Vector Notation
38:42
Calculating the Cross Product Matrix Notation
39:18
Calculating the Cross Product Matrix Notation
39:19
Example VII: Find the Cross Product of the Following Vectors
42:09
Cross Product Properties
45:16
Cross Product Properties
45:17
Units
46:41
Fundamental Units
46:42
Derived units
47:13
Example IX: Dimensional Analysis
47:21
Calculus
49:05
Calculus
49:06
Differential Calculus
49:49
Differentiation & Derivative
49:50
Example X: Derivatives
51:21
Integral Calculus
53:03
Integration
53:04
Integral
53:11
Integration & Derivation are Inverse Functions
53:16
Determine the Original Function
53:37
Common Integrations
54:45
Common Integrations
54:46
Example XI: Integrals
55:17
Example XII: Calculus Applications
58:32
Section 2: Kinematics
Describing Motion I

23m 47s

Intro
0:00
Objectives
0:10
Position / Displacement
0:39
Object's Position
0:40
Position Vector
0:45
Displacement
0:56
Position & Displacement are Vectors
1:05
Position & Displacement in 1 Dimension
1:11
Example I: Distance & Displacement
1:21
Average Speed
2:14
Average Speed
2:15
Average Speed is Scalar
2:27
Average Velocity
2:39
Average Velocity
2:40
Average Velocity is a Vector
2:57
Example II: Speed vs. Velocity
3:16
Example II: Deer's Average Speed
3:17
Example II: Deer's Average Velocity
3:48
Example III: Chuck the Hungry Squirrel
4:21
Example III: Chuck's Distance Traveled
4:22
Example III: Chuck's Displacement
4:43
Example III: Chuck's Average Speed
5:25
Example III: Chuck's Average Velocity
5:39
Acceleration
6:11
Acceleration: Definition & Equation
6:12
Acceleration: Units
6:19
Relationship of Acceleration to Velocity
6:52
Example IV: Acceleration Problem
7:05
The Position Vector
7:39
The Position Vector
7:40
Average Velocity
9:35
Average Velocity
9:36
Instantaneous Velocity
11:20
Instantaneous Velocity
11:21
Instantaneous Velocity is the Derivative of Position with Respect to Time
11:35
Area Under the Velocity-time Graph
12:08
Acceleration
12:36
More on Acceleration
12:37
Average Acceleration
13:11
Velocity vs. Time Graph
13:14
Graph Transformations
13:59
Graphical Analysis of Motion
14:00
Velocity and acceleration in 2D
14:35
Velocity Vector in 2D
14:39
Acceleration Vector in 2D
15:26
Polynomial Derivatives
16:10
Polynomial Derivatives
16:11
Example V: Polynomial Kinematics
16:31
Example VI: Velocity Function
17:54
Example VI: Part A - Determine the Acceleration at t=1 Second
17:55
Example VI: Part B - Determine the Displacement between t=0 and t=5 Seconds
18:33
Example VII: Tortoise and Hare
20:14
Example VIII: d-t Graphs
22:40
Describing Motion II

36m 47s

Intro
0:00
Objectives
0:09
Special Case: Constant Acceleration
0:31
Constant Acceleration & Kinematic Equations
0:32
Deriving the Kinematic Equations
1:28
V = V₀ + at
1:39
∆x = V₀t +(1/2)at²
2:03
V² = V₀² +2a∆x
4:05
Problem Solving Steps
7:02
Step 1
7:13
Step 2
7:18
Step 3
7:27
Step 4
7:30
Step 5
7:31
Example IX: Horizontal Kinematics
7:38
Example X: Vertical Kinematics
9:45
Example XI: 2 Step Problem
11:23
Example XII: Acceleration Problem
15:01
Example XIII: Particle Diagrams
15:57
Example XIV: Particle Diagrams
17:36
18:46
Free Fall
22:56
Free Fall
22:57
Air Resistance
23:24
Air Resistance
23:25
Acceleration Due to Gravity
23:48
Acceleration Due to Gravity
23:49
Objects Falling From Rest
24:18
Objects Falling From Rest
24:19
Example XVI: Falling Objects
24:55
Objects Launched Upward
26:01
Objects Launched Upward
26:02
Example XVII: Ball Thrown Upward
27:16
Example XVIII: Height of a Jump
27:48
Example XIX: Ball Thrown Downward
31:10
Example XX: Maximum Height
32:27
Example XXI: Catch-Up Problem
33:53
Example XXII: Ranking Max Height
35:52
Projectile Motion

30m 34s

Intro
0:00
Objectives
0:07
What is a Projectile?
0:28
What is a Projectile?
0:29
Path of a Projectile
0:58
Path of a Projectile
0:59
Independence of Motion
2:45
Vertical & Horizontal Motion
2:46
Example I: Horizontal Launch
3:14
Example II: Parabolic Path
7:20
Angled Projectiles
8:01
Angled Projectiles
8:02
Example III: Human Cannonball
10:05
Example IV: Motion Graphs
14:39
Graphing Projectile Motion
19:05
Horizontal Equation
19:06
Vertical Equation
19:46
Example V: Arrow Fired from Tower
21:28
Example VI: Arrow Fired from Tower
24:10
Example VII: Launch from a Height
24:40
Example VIII: Acceleration of a Projectile
29:49
Circular & Relative Motion

30m 24s

Intro
0:00
Objectives
0:08
0:32
Degrees
0:35
0:40
1:08
Example I: Part A - Convert 90 Degrees to Radians
1:09
Example I: Part B - Convert 6 Radians to Degrees
2:08
Linear vs. Angular Displacement
2:38
Linear Displacement
2:39
Angular Displacement
2:52
Linear vs. Angular Velocity
3:18
Linear Velocity
3:19
Angular Velocity
3:25
Direction of Angular Velocity
4:36
Direction of Angular Velocity
4:37
Converting Linear to Angular Velocity
5:05
Converting Linear to Angular Velocity
5:06
Example II: Earth's Angular Velocity
6:12
Linear vs. Angular Acceleration
7:26
Linear Acceleration
7:27
Angular Acceleration
7:32
Centripetal Acceleration
8:05
Expressing Position Vector in Terms of Unit Vectors
8:06
Velocity
10:00
Centripetal Acceleration
11:14
Magnitude of Centripetal Acceleration
13:24
Example III: Angular Velocity & Centripetal Acceleration
14:02
Example IV: Moon's Orbit
15:03
Reference Frames
17:44
Reference Frames
17:45
Laws of Physics
18:00
Motion at Rest vs. Motion at a Constant Velocity
18:21
Motion is Relative
19:20
Reference Frame: Sitting in a Lawn Chair
19:21
Reference Frame: Sitting on a Train
19:56
Calculating Relative Velocities
20:19
Calculating Relative Velocities
20:20
Example: Calculating Relative Velocities
20:57
Example V: Man on a Train
23:19
Example VI: Airspeed
24:56
Example VII: 2-D Relative Motion
26:12
Example VIII: Relative Velocity w/ Direction
28:32
Section 3: Dynamics
Newton's First Law & Free Body Diagrams

23m 57s

Intro
0:00
Objectives
0:11
Newton's 1st Law of Motion
0:28
Newton's 1st Law of Motion
0:29
Force
1:16
Definition of Force
1:17
Units of Force
1:20
How Much is a Newton?
1:25
Contact Forces
1:47
Field Forces
2:32
What is a Net Force?
2:53
What is a Net Force?
2:54
What Does It Mean?
4:35
What Does It Mean?
4:36
Objects at Rest
4:52
Objects at Rest
4:53
Objects in Motion
5:12
Objects in Motion
5:13
Equilibrium
6:03
Static Equilibrium
6:04
Mechanical Equilibrium
6:22
Translational Equilibrium
6:38
Inertia
6:48
Inertia
6:49
Inertial Mass
6:58
Gravitational Mass
7:11
Example I: Inertia
7:40
Example II: Inertia
8:03
Example III: Translational Equilibrium
8:25
Example IV: Net Force
9:19
Free Body Diagrams
10:34
Free Body Diagrams Overview
10:35
Falling Elephant: Free Body Diagram
10:53
Free Body Diagram Neglecting Air Resistance
10:54
Free Body Diagram Including Air Resistance
11:22
Soda on Table
11:54
Free Body Diagram for a Glass of Soda Sitting on a Table
11:55
Free Body Diagram for Box on Ramp
13:38
Free Body Diagram for Box on Ramp
13:39
Pseudo- Free Body Diagram
15:26
Example V: Translational Equilibrium
18:35
Newton's Second & Third Laws of Motion

23m 57s

Intro
0:00
Objectives
0:09
Newton's 2nd Law of Motion
0:36
Newton's 2nd Law of Motion
0:37
Applying Newton's 2nd Law
1:12
Step 1
1:13
Step 2
1:18
Step 3
1:27
Step 4
1:36
Example I: Block on a Surface
1:42
Example II: Concurrent Forces
2:42
Mass vs. Weight
4:09
Mass
4:10
Weight
4:28
Example III: Mass vs. Weight
4:45
Example IV: Translational Equilibrium
6:43
Example V: Translational Equilibrium
8:23
Example VI: Determining Acceleration
10:13
Example VII: Stopping a Baseball
12:38
Example VIII: Steel Beams
14:11
Example IX: Tension Between Blocks
17:03
Example X: Banked Curves
18:57
Example XI: Tension in Cords
24:03
Example XII: Graphical Interpretation
27:13
Example XIII: Force from Velocity
28:12
Newton's 3rd Law
29:16
Newton's 3rd Law
29:17
Examples - Newton's 3rd Law
30:01
Examples - Newton's 3rd Law
30:02
Action-Reaction Pairs
30:40
Girl Kicking Soccer Ball
30:41
Rocket Ship in Space
31:02
Gravity on You
31:23
Example XIV: Force of Gravity
32:11
Example XV: Sailboat
32:38
Example XVI: Hammer and Nail
33:18
Example XVII: Net Force
33:47
Friction

20m 41s

Intro
0:00
Objectives
0:06
Coefficient of Friction
0:21
Coefficient of Friction
0:22
Approximate Coefficients of Friction
0:44
Kinetic or Static?
1:21
Sled Sliding Down a Snowy Hill
1:22
Refrigerator at Rest that You Want to Move
1:32
Car with Tires Rolling Freely
1:49
Car Skidding Across Pavement
2:01
Example I: Car Sliding
2:21
Example II: Block on Incline
3:04
Calculating the Force of Friction
3:33
Calculating the Force of Friction
3:34
Example III: Finding the Frictional Force
4:02
Example IV: Box on Wood Surface
5:34
Example V: Static vs. Kinetic Friction
7:35
Example VI: Drag Force on Airplane
7:58
Example VII: Pulling a Sled
8:41
Example VIII: AP-C 2007 FR1
13:23
Example VIII: Part A
13:24
Example VIII: Part B
14:40
Example VIII: Part C
15:19
Example VIII: Part D
17:08
Example VIII: Part E
18:24
Retarding & Drag Forces

32m 10s

Intro
0:00
Objectives
0:07
Retarding Forces
0:41
Retarding Forces
0:42
The Skydiver
1:30
Drag Forces on a Free-falling Object
1:31
Velocity as a Function of Time
5:31
Velocity as a Function of Time
5:32
Velocity as a Function of Time, cont.
12:27
Acceleration
12:28
Velocity as a Function of Time, cont.
15:16
Graph: Acceleration vs. Time
16:06
Graph: Velocity vs. Time
16:40
Graph: Displacement vs. Time
17:04
Example I: AP-C 2005 FR1
17:43
Example I: Part A
17:44
Example I: Part B
19:17
Example I: Part C
20:17
Example I: Part D
21:09
Example I: Part E
22:42
Example II: AP-C 2013 FR2
24:26
Example II: Part A
24:27
Example II: Part B
25:25
Example II: Part C
26:22
Example II: Part D
27:04
Example II: Part E
30:50
Ramps & Inclines

20m 31s

Intro
0:00
Objectives
0:06
Drawing Free Body Diagrams for Ramps
0:32
Step 1: Choose the Object & Draw It as a Dot or Box
0:33
Step 2: Draw and Label all the External Forces
0:39
Step 3: Sketch a Coordinate System
0:42
Example: Object on a Ramp
0:52
Pseudo-Free Body Diagrams
2:06
Pseudo-Free Body Diagrams
2:07
Redraw Diagram with All Forces Parallel to Axes
2:18
Box on a Ramp
4:08
Free Body Diagram for Box on a Ramp
4:09
Pseudo-Free Body Diagram for Box on a Ramp
4:54
Example I: Box at Rest
6:13
Example II: Box Held By Force
6:35
Example III: Truck on a Hill
8:46
Example IV: Force Up a Ramp
9:29
Example V: Acceleration Down a Ramp
12:01
Example VI: Able of Repose
13:59
Example VII: Sledding
17:03
Atwood Machines

24m 58s

Intro
0:00
Objectives
0:07
What is an Atwood Machine?
0:25
What is an Atwood Machine?
0:26
Properties of Atwood Machines
1:03
Ideal Pulleys are Frictionless and Massless
1:04
Tension is Constant
1:14
Setup for Atwood Machines
1:26
Setup for Atwood Machines
1:27
Solving Atwood Machine Problems
1:52
Solving Atwood Machine Problems
1:53
Alternate Solution
5:24
Analyze the System as a Whole
5:25
Example I: Basic Atwood Machine
7:31
Example II: Moving Masses
9:59
Example III: Masses and Pulley on a Table
13:32
Example IV: Mass and Pulley on a Ramp
15:47
Example V: Ranking Atwood Machines
19:50
Section 4: Work, Energy, & Power
Work

37m 34s

Intro
0:00
Objectives
0:07
What is Work?
0:36
What is Work?
0:37
Units of Work
1:09
Work in One Dimension
1:31
Work in One Dimension
1:32
Examples of Work
2:19
Stuntman in a Jet Pack
2:20
A Girl Struggles to Push Her Stalled Car
2:50
A Child in a Ghost Costume Carries a Bag of Halloween Candy Across the Yard
3:24
Example I: Moving a Refrigerator
4:03
Example II: Liberating a Car
4:53
Example III: Lifting Box
5:30
Example IV: Pulling a Wagon
6:13
Example V: Ranking Work on Carts
7:13
Non-Constant Forces
12:21
Non-Constant Forces
12:22
Force vs. Displacement Graphs
13:49
Force vs. Displacement Graphs
13:50
Hooke's Law
14:41
Hooke's Law
14:42
Determining the Spring Constant
15:38
Slope of the Graph Gives the Spring Constant, k
15:39
Work Done in Compressing the Spring
16:34
Find the Work Done in Compressing the String
16:35
Example VI: Finding Spring Constant
17:21
Example VII: Calculating Spring Constant
19:48
Example VIII: Hooke's Law
20:30
Example IX: Non-Linear Spring
22:18
Work in Multiple Dimensions
23:52
Work in Multiple Dimensions
23:53
Work-Energy Theorem
25:25
Work-Energy Theorem
25:26
Example X: Work-Energy Theorem
28:35
Example XI: Work Done on Moving Carts
30:46
Example XII: Velocity from an F-d Graph
35:01
Energy & Conservative Forces

28m 4s

Intro
0:00
Objectives
0:08
Energy Transformations
0:31
Energy Transformations
0:32
Work-Energy Theorem
0:57
Kinetic Energy
1:12
Kinetic Energy: Definition
1:13
Kinetic Energy: Equation
1:55
Example I: Frog-O-Cycle
2:07
Potential Energy
2:46
Types of Potential Energy
2:47
A Potential Energy Requires an Interaction between Objects
3:29
Internal energy
3:50
Internal Energy
3:51
Types of Energy
4:37
Types of Potential & Kinetic Energy
4:38
Gravitational Potential Energy
5:42
Gravitational Potential Energy
5:43
Example II: Potential Energy
7:27
Example III: Kinetic and Potential Energy
8:16
Example IV: Pendulum
9:09
Conservative Forces
11:37
Conservative Forces Overview
11:38
Type of Conservative Forces
12:42
Types of Non-conservative Forces
13:02
Work Done by Conservative Forces
13:28
Work Done by Conservative Forces
13:29
Newton's Law of Universal Gravitation
14:18
Gravitational Force of Attraction between Any Two Objects with Mass
14:19
Gravitational Potential Energy
15:27
Gravitational Potential Energy
15:28
Elastic Potential Energy
17:36
Elastic Potential Energy
17:37
Force from Potential Energy
18:51
Force from Potential Energy
18:52
Gravitational Force from the Gravitational Potential Energy
20:46
Gravitational Force from the Gravitational Potential Energy
20:47
Hooke's Law from Potential Energy
22:04
Hooke's Law from Potential Energy
22:05
Summary
23:16
Summary
23:17
Example V: Kinetic Energy of a Mass
24:40
Example VI: Force from Potential Energy
25:48
Example VII: Work on a Spinning Disc
26:54
Conservation of Energy

54m 56s

Intro
0:00
Objectives
0:09
Conservation of Mechanical Energy
0:32
Consider a Single Conservative Force Doing Work on a Closed System
0:33
Non-Conservative Forces
1:40
Non-Conservative Forces
1:41
Work Done by a Non-conservative Force
1:47
Formula: Total Energy
1:54
Formula: Total Mechanical Energy
2:04
Example I: Falling Mass
2:15
Example II: Law of Conservation of Energy
4:07
Example III: The Pendulum
6:34
Example IV: Cart Compressing a Spring
10:12
Example V: Cart Compressing a Spring
11:12
Example V: Part A - Potential Energy Stored in the Compressed Spring
11:13
Example V: Part B - Maximum Vertical Height
12:01
Example VI: Car Skidding to a Stop
13:05
Example VII: Block on Ramp
14:22
Example VIII: Energy Transfers
16:15
Example IX: Roller Coaster
20:04
Example X: Bungee Jumper
23:32
Example X: Part A - Speed of the Jumper at a Height of 15 Meters Above the Ground
24:48
Example X: Part B - Speed of the Jumper at a Height of 30 Meters Above the Ground
26:53
Example X: Part C - How Close Does the Jumper Get to the Ground?
28:28
Example XI: AP-C 2002 FR3
30:28
Example XI: Part A
30:59
Example XI: Part B
31:54
Example XI: Part C
32:50
Example XI: Part D & E
33:52
Example XII: AP-C 2007 FR3
35:24
Example XII: Part A
35:52
Example XII: Part B
36:27
Example XII: Part C
37:48
Example XII: Part D
39:32
Example XIII: AP-C 2010 FR1
41:07
Example XIII: Part A
41:34
Example XIII: Part B
43:05
Example XIII: Part C
45:24
Example XIII: Part D
47:18
Example XIV: AP-C 2013 FR1
48:25
Example XIV: Part A
48:50
Example XIV: Part B
49:31
Example XIV: Part C
51:27
Example XIV: Part D
52:46
Example XIV: Part E
53:25
Power

16m 44s

Intro
0:00
Objectives
0:06
Defining Power
0:20
Definition of Power
0:21
Units of Power
0:27
Average Power
0:43
Instantaneous Power
1:03
Instantaneous Power
1:04
Example I: Horizontal Box
2:07
Example II: Accelerating Truck
4:48
Example III: Motors Delivering Power
6:00
Example IV: Power Up a Ramp
7:00
Example V: Power from Position Function
8:51
Example VI: Motorcycle Stopping
10:48
Example VII: AP-C 2003 FR1
11:52
Example VII: Part A
11:53
Example VII: Part B
12:50
Example VII: Part C
14:36
Example VII: Part D
15:52
Section 5: Momentum
Momentum & Impulse

13m 9s

Intro
0:00
Objectives
0:07
Momentum
0:39
Definition of Momentum
0:40
Total Momentum
1:00
Formula for Momentum
1:05
Units of Momentum
1:11
Example I: Changing Momentum
1:18
Impulse
2:27
Impulse
2:28
Example II: Impulse
2:41
Relationship Between Force and ∆p (Impulse)
3:36
Relationship Between Force and ∆p (Impulse)
3:37
Example III: Force from Momentum
4:37
Impulse-Momentum Theorem
5:14
Impulse-Momentum Theorem
5:15
Example IV: Impulse-Momentum
6:26
Example V: Water Gun & Horizontal Force
7:56
Impulse from F-t Graphs
8:53
Impulse from F-t Graphs
8:54
Example VI: Non-constant Forces
9:16
Example VII: F-t Graph
10:01
Example VIII: Impulse from Force
11:19
Conservation of Linear Momentum

46m 30s

Intro
0:00
Objectives
0:08
Conservation of Linear Momentum
0:28
In an Isolated System
0:29
In Any Closed System
0:37
Direct Outcome of Newton's 3rd Law of Motion
0:47
Collisions and Explosions
1:07
Collisions and Explosions
1:08
The Law of Conservation of Linear Momentum
1:25
Solving Momentum Problems
1:35
Solving Momentum Problems
1:36
Types of Collisions
2:08
Elastic Collision
2:09
Inelastic Collision
2:34
Example I: Traffic Collision
3:00
Example II: Collision of Two Moving Objects
6:55
Example III: Recoil Velocity
9:47
Example IV: Atomic Collision
12:12
Example V: Collision in Multiple Dimensions
18:11
Example VI: AP-C 2001 FR1
25:16
Example VI: Part A
25:33
Example VI: Part B
26:44
Example VI: Part C
28:17
Example VI: Part D
28:58
Example VII: AP-C 2002 FR1
30:10
Example VII: Part A
30:20
Example VII: Part B
32:14
Example VII: Part C
34:25
Example VII: Part D
36:17
Example VIII: AP-C 2014 FR1
38:55
Example VIII: Part A
39:28
Example VIII: Part B
41:00
Example VIII: Part C
42:57
Example VIII: Part D
44:20
Center of Mass

28m 26s

Intro
0:00
Objectives
0:07
Center of Mass
0:45
Center of Mass
0:46
Finding Center of Mass by Inspection
1:25
For Uniform Density Objects
1:26
For Objects with Multiple Parts
1:36
For Irregular Objects
1:44
Example I: Center of Mass by Inspection
2:06
Calculating Center of Mass for Systems of Particles
2:25
Calculating Center of Mass for Systems of Particles
2:26
Example II: Center of Mass (1D)
3:15
Example III: Center of Mass of Continuous System
4:29
Example IV: Center of Mass (2D)
6:00
Finding Center of Mass by Integration
7:38
Finding Center of Mass by Integration
7:39
Example V: Center of Mass of a Uniform Rod
8:10
Example VI: Center of Mass of a Non-Uniform Rod
11:40
Center of Mass Relationships
14:44
Center of Mass Relationships
14:45
Center of Gravity
17:36
Center of Gravity
17:37
Uniform Gravitational Field vs. Non-uniform Gravitational Field
17:53
Example VII: AP-C 2004 FR1
18:26
Example VII: Part A
18:45
Example VII: Part B
19:38
Example VII: Part C
21:03
Example VII: Part D
22:04
Example VII: Part E
24:52
Section 6: Uniform Circular Motion
Uniform Circular Motion

21m 36s

Intro
0:00
Objectives
0:08
Uniform Circular Motion
0:42
Distance Around the Circle for Objects Traveling in a Circular Path at Constant Speed
0:51
Average Speed for Objects Traveling in a Circular Path at Constant Speed
1:15
Frequency
1:42
Definition of Frequency
1:43
Symbol of Frequency
1:46
Units of Frequency
1:49
Period
2:04
Period
2:05
Frequency and Period
2:19
Frequency and Period
2:20
Example I: Race Car
2:32
Example II: Toy Train
3:22
Example III: Round-A-Bout
4:07
Example III: Part A - Period of the Motion
4:08
Example III: Part B- Frequency of the Motion
4:43
Example III: Part C- Speed at Which Alan Revolves
4:58
Uniform Circular Motion
5:28
Is an Object Undergoing Uniform Circular Motion Accelerating?
5:29
Direction of Centripetal Acceleration
6:21
Direction of Centripetal Acceleration
6:22
Magnitude of Centripetal Acceleration
8:23
Magnitude of Centripetal Acceleration
8:24
Example IV: Car on a Track
8:39
Centripetal Force
10:14
Centripetal Force
10:15
Calculating Centripetal Force
11:47
Calculating Centripetal Force
11:48
Example V: Acceleration
12:41
Example VI: Direction of Centripetal Acceleration
13:44
Example VII: Loss of Centripetal Force
14:03
Example VIII: Bucket in Horizontal Circle
14:44
Example IX: Bucket in Vertical Circle
15:24
Example X: Demon Drop
17:38
Example X: Question 1
18:02
Example X: Question 2
18:25
Example X: Question 3
19:22
Example X: Question 4
20:13
Section 7: Rotational Motion
Rotational Kinematics

32m 52s

Intro
0:00
Objectives
0:07
0:35
Once Around a Circle: In Degrees
0:36
Once Around a Circle: In Radians
0:48
0:51
1:08
Example I: Convert 90° to Radians
1:09
Example I: Convert 6 Radians to Degree
1:23
Linear vs. Angular Displacement
1:43
Linear Displacement
1:44
Angular Displacement
1:51
Linear vs. Angular Velocity
2:04
Linear Velocity
2:05
Angular Velocity
2:10
Direction of Angular Velocity
2:28
Direction of Angular Velocity
2:29
Converting Linear to Angular Velocity
2:58
Converting Linear to Angular Velocity
2:59
Example II: Angular Velocity of Earth
3:51
Linear vs. Angular Acceleration
4:35
Linear Acceleration
4:36
Angular Acceleration
4:42
Example III: Angular Acceleration
5:09
Kinematic Variable Parallels
6:30
Kinematic Variable Parallels: Translational & Angular
6:31
Variable Translations
7:00
Variable Translations: Translational & Angular
7:01
Kinematic Equation Parallels
7:38
Kinematic Equation Parallels: Translational & Rotational
7:39
Example IV: Deriving Centripetal Acceleration
8:29
Example V: Angular Velocity
13:24
Example V: Part A
13:25
Example V: Part B
14:15
Example VI: Wheel in Motion
14:39
Example VII: AP-C 2003 FR3
16:23
Example VII: Part A
16:38
Example VII: Part B
17:34
Example VII: Part C
24:02
Example VIII: AP-C 2014 FR2
25:35
Example VIII: Part A
25:47
Example VIII: Part B
26:28
Example VIII: Part C
27:48
Example VIII: Part D
28:26
Example VIII: Part E
29:16
Moment of Inertia

24m

Intro
0:00
Objectives
0:07
Types of Inertia
0:34
Inertial Mass
0:35
Moment of Inertia
0:44
Kinetic Energy of a Rotating Disc
1:25
Kinetic Energy of a Rotating Disc
1:26
Calculating Moment of Inertia (I)
5:32
Calculating Moment of Inertia (I)
5:33
Moment of Inertia for Common Objects
5:49
Moment of Inertia for Common Objects
5:50
Example I: Point Masses
6:46
Example II: Uniform Rod
9:09
Example III: Solid Cylinder
13:07
Parallel Axis Theorem (PAT)
17:33
Parallel Axis Theorem (PAT)
17:34
Example IV: Calculating I Using the Parallel Axis Theorem
18:39
Example V: Hollow Sphere
20:18
Example VI: Long Thin Rod
20:55
Example VII: Ranking Moment of Inertia
21:50
Example VIII: Adjusting Moment of Inertia
22:39
Torque

26m 9s

Intro
0:00
Objectives
0:06
Torque
0:18
Definition of Torque
0:19
Torque & Rotation
0:26
Lever Arm ( r )
0:30
Example: Wrench
0:39
Direction of the Torque Vector
1:45
Direction of the Torque Vector
1:46
Finding Direction Using the Right-hand Rule
1:53
Newton's 2nd Law: Translational vs. Rotational
2:20
Newton's 2nd Law: Translational vs. Rotational
2:21
Equilibrium
3:17
Static Equilibrium
3:18
Dynamic Equilibrium
3:30
Example I: See-Saw Problem
3:46
Example II: Beam Problem
7:12
Example III: Pulley with Mass
10:34
Example IV: Net Torque
13:46
Example V: Ranking Torque
15:29
Example VI: Ranking Angular Acceleration
16:25
Example VII: Café Sign
17:19
Example VIII: AP-C 2008 FR2
19:44
Example VIII: Part A
20:12
Example VIII: Part B
21:08
Example VIII: Part C
22:36
Example VIII: Part D
24:37
Rotational Dynamics

56m 58s

Intro
0:00
Objectives
0:08
Conservation of Energy
0:48
Translational Kinetic Energy
0:49
Rotational Kinetic Energy
0:54
Total Kinetic Energy
1:03
Example I: Disc Rolling Down an Incline
1:10
Rotational Dynamics
4:25
Rotational Dynamics
4:26
Example II: Strings with Massive Pulleys
4:37
Example III: Rolling without Slipping
9:13
Example IV: Rolling with Slipping
13:45
Example V: Amusement Park Swing
22:49
Example VI: AP-C 2002 FR2
26:27
Example VI: Part A
26:48
Example VI: Part B
27:30
Example VI: Part C
29:51
Example VI: Part D
30:50
Example VII: AP-C 2006 FR3
31:39
Example VII: Part A
31:49
Example VII: Part B
36:20
Example VII: Part C
37:14
Example VII: Part D
38:48
Example VIII: AP-C 2010 FR2
39:40
Example VIII: Part A
39:46
Example VIII: Part B
40:44
Example VIII: Part C
44:31
Example VIII: Part D
46:44
Example IX: AP-C 2013 FR3
48:27
Example IX: Part A
48:47
Example IX: Part B
50:33
Example IX: Part C
53:28
Example IX: Part D
54:15
Example IX: Part E
56:20
Angular Momentum

33m 2s

Intro
0:00
Objectives
0:09
Linear Momentum
0:44
Definition of Linear Momentum
0:45
Total Angular Momentum
0:52
p = mv
0:59
Angular Momentum
1:08
Definition of Angular Momentum
1:09
Total Angular Momentum
1:21
A Mass with Velocity v Moving at Some Position r
1:29
Calculating Angular Momentum
1:44
Calculating Angular Momentum
1:45
Spin Angular Momentum
4:17
Spin Angular Momentum
4:18
Example I: Object in Circular Orbit
4:51
Example II: Angular Momentum of a Point Particle
6:34
Angular Momentum and Net Torque
9:03
Angular Momentum and Net Torque
9:04
Conservation of Angular Momentum
11:53
Conservation of Angular Momentum
11:54
Example III: Ice Skater Problem
12:20
Example IV: Combining Spinning Discs
13:52
Example V: Catching While Rotating
15:13
Example VI: Changes in Angular Momentum
16:47
Example VII: AP-C 2005 FR3
17:37
Example VII: Part A
18:12
Example VII: Part B
18:32
Example VII: Part C
19:53
Example VII: Part D
21:52
Example VIII: AP-C 2014 FR3
24:23
Example VIII: Part A
24:31
Example VIII: Part B
25:33
Example VIII: Part C
26:58
Example VIII: Part D
28:24
Example VIII: Part E
30:42
Section 8: Oscillations
Oscillations

1h 1m 12s

Intro
0:00
Objectives
0:08
Simple Harmonic Motion
0:45
Simple Harmonic Motion
0:46
Circular Motion vs. Simple Harmonic Motion (SHM)
1:39
Circular Motion vs. Simple Harmonic Motion (SHM)
1:40
Position, Velocity, & Acceleration
4:55
Position
4:56
Velocity
5:12
Acceleration
5:49
Frequency and Period
6:37
Frequency
6:42
Period
6:49
Angular Frequency
7:05
Angular Frequency
7:06
Example I: Oscillating System
7:37
Example I: Determine the Object's Angular Frequency
7:38
Example I: What is the Object's Position at Time t = 10s?
8:16
Example I: At What Time is the Object at x = 0.1m?
9:10
Mass on a Spring
10:17
Mass on a Spring
10:18
Example II: Analysis of Spring-Block System
11:34
Example III: Spring-Block ranking
12:53
General Form of Simple Harmonic Motion
14:41
General Form of Simple Harmonic Motion
14:42
Graphing Simple Harmonic Motion (SHM)
15:22
Graphing Simple Harmonic Motion (SHM)
15:23
Energy of Simple Harmonic Motion (SHM)
15:49
Energy of Simple Harmonic Motion (SHM)
15:50
Horizontal Spring Oscillator
19:24
Horizontal Spring Oscillator
19:25
Vertical Spring Oscillator
20:58
Vertical Spring Oscillator
20:59
Springs in Series
23:30
Springs in Series
23:31
Springs in Parallel
26:08
Springs in Parallel
26:09
The Pendulum
26:59
The Pendulum
27:00
Energy and the Simple Pendulum
27:46
Energy and the Simple Pendulum
27:47
Frequency and Period of a Pendulum
30:16
Frequency and Period of a Pendulum
30:17
Example IV: Deriving Period of a Simple Pendulum
31:42
Example V: Deriving Period of a Physical Pendulum
35:20
Example VI: Summary of Spring-Block System
38:16
Example VII: Harmonic Oscillator Analysis
44:14
Example VII: Spring Constant
44:24
Example VII: Total Energy
44:45
Example VII: Speed at the Equilibrium Position
45:05
Example VII: Speed at x = 0.30 Meters
45:37
Example VII: Speed at x = -0.40 Meter
46:46
Example VII: Acceleration at the Equilibrium Position
47:21
Example VII: Magnitude of Acceleration at x = 0.50 Meters
47:35
Example VII: Net Force at the Equilibrium Position
48:04
Example VII: Net Force at x = 0.25 Meter
48:20
Example VII: Where does Kinetic Energy = Potential Energy?
48:33
Example VIII: Ranking Spring Systems
49:35
Example IX: Vertical Spring Block Oscillator
51:45
Example X: Ranking Period of Pendulum
53:50
Example XI: AP-C 2009 FR2
54:50
Example XI: Part A
54:58
Example XI: Part B
57:57
Example XI: Part C
59:11
Example XII: AP-C 2010 FR3
1:00:18
Example XII: Part A
1:00:49
Example XII: Part B
1:02:47
Example XII: Part C
1:04:30
Example XII: Part D
1:05:53
Example XII: Part E
1:08:13
Section 9: Gravity & Orbits
Gravity & Orbits

34m 59s

Intro
0:00
Objectives
0:07
Newton's Law of Universal Gravitation
0:45
Newton's Law of Universal Gravitation
0:46
Example I: Gravitational Force Between Earth and Sun
2:24
Example II: Two Satellites
3:39
Gravitational Field Strength
4:23
Gravitational Field Strength
4:24
Example III: Weight on Another Planet
6:22
Example IV: Gravitational Field of a Hollow Shell
7:31
Example V: Gravitational Field Inside a Solid Sphere
8:33
Velocity in Circular Orbit
12:05
Velocity in Circular Orbit
12:06
Period and Frequency for Circular Orbits
13:56
Period and Frequency for Circular Orbits
13:57
Mechanical Energy for Circular Orbits
16:11
Mechanical Energy for Circular Orbits
16:12
Escape Velocity
17:48
Escape Velocity
17:49
Kepler's 1st Law of Planetary Motion
19:41
Keller's 1st Law of Planetary Motion
19:42
Kepler's 2nd Law of Planetary Motion
20:05
Keller's 2nd Law of Planetary Motion
20:06
Kepler's 3rd Law of Planetary Motion
20:57
Ratio of the Squares of the Periods of Two Planets
20:58
Ratio of the Squares of the Periods to the Cubes of Their Semi-major Axes
21:41
Total Mechanical Energy for an Elliptical Orbit
21:57
Total Mechanical Energy for an Elliptical Orbit
21:58
Velocity and Radius for an Elliptical Orbit
22:35
Velocity and Radius for an Elliptical Orbit
22:36
Example VI: Rocket Launched Vertically
24:26
Example VII: AP-C 2007 FR2
28:16
Example VII: Part A
28:35
Example VII: Part B
29:51
Example VII: Part C
31:14
Example VII: Part D
32:23
Example VII: Part E
33:16
Section 10: Sample AP Exam
1998 AP Practice Exam: Multiple Choice

28m 11s

Intro
0:00
Problem 1
0:30
Problem 2
0:51
Problem 3
1:25
Problem 4
2:00
Problem 5
3:05
Problem 6
4:19
Problem 7
4:48
Problem 8
5:18
Problem 9
5:38
Problem 10
6:26
Problem 11
7:21
Problem 12
8:08
Problem 13
8:35
Problem 14
9:20
Problem 15
10:09
Problem 16
10:25
Problem 17
11:30
Problem 18
12:27
Problem 19
13:00
Problem 20
14:40
Problem 21
15:44
Problem 22
16:42
Problem 23
17:35
Problem 24
17:54
Problem 25
18:32
Problem 26
19:08
Problem 27
20:56
Problem 28
22:19
Problem 29
22:36
Problem 30
23:18
Problem 31
24:06
Problem 32
24:40
1998 AP Practice Exam: Free Response Questions (FRQ)

28m 11s

Intro
0:00
Question 1
0:15
Part A: I
0:16
Part A: II
0:46
Part A: III
1:13
Part B
1:40
Part C
2:49
Part D: I
4:46
Part D: II
5:15
Question 2
5:46
Part A: I
6:13
Part A: II
7:05
Part B: I
7:48
Part B: II
8:42
Part B: III
9:03
Part B: IV
9:26
Part B: V
11:32
Question 3
13:30
Part A: I
13:50
Part A: II
14:16
Part A: III
14:38
Part A: IV
14:56
Part A: V
15:36
Part B
16:11
Part C
17:00
Part D: I
19:56
Part D: II
21:08
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• ## Related Books 4 answersLast reply by: Cyrus SeyrafiSun Nov 10, 2019 8:44 PMPost by Cyrus Seyrafi on November 9, 2019In example 13, how does velocity's being proportional to time squared affect the the force graph? Or does it? 1 answer Last reply by: Professor Dan FullertonWed Oct 19, 2016 7:43 AMPost by James Glass on October 19, 2016Hello,In example 10 (x), the problem with the banked curve, why doesn't (mg)sin(theta) somehow contribute to the force due to centripetal acceleration (m(v^2/r)? I think I understand why the y component of the centripetal force is (Fnormal)cos(theta).Thanks. 0 answersPost by James Glass on October 19, 2016Hello,In example 10 (x), the problem with the banked curve, why doesn't (mg)sin(theta) somehow contribute to the force due to centripetal acceleration (m(v^2/r)? I think I understand why the y component of the centripetal force is (Fnormal)cos(theta).Thanks. 2 answersLast reply by: Cathy ZhaoSat Aug 13, 2016 8:51 PMPost by Cathy Zhao on August 12, 2016On example 9, why the acceleration of T2 equals to that of T1? 2 answersLast reply by: Cathy ZhaoSat Aug 13, 2016 8:51 PMPost by Cathy Zhao on August 12, 2016On example 6, why there is no acceleration in the y direction? 1 answer Last reply by: Professor Dan FullertonFri Aug 12, 2016 1:07 PMPost by Dukaiwen Zhao on August 12, 2016On example 5 (translational equilibrium), Answer choice D should be 5 N instead of 4 N right? 4 answersLast reply by: Hemant SrivastavaSat Jul 16, 2016 7:35 PMPost by Hemant Srivastava on July 15, 2016On example 8, shouldn't the gravity be -9.8 m/s^2? 1 answer Last reply by: Professor Dan FullertonMon Nov 23, 2015 7:16 AMPost by Zhe Tian on November 19, 2015Why is it on practice problem 9 you don't consider tension T2 for T1? Why isn't T1-T2=ma correct? 1 answer Last reply by: Professor Dan FullertonSun May 3, 2015 6:32 PMPost by Nitin Prasad on May 3, 2015In the block on a surface problem, why did you only find the horizontal component of acceleration? Shouldn't you also find the vertical component and take the vector sum? 2 answersLast reply by: BRAD POOLETue Mar 31, 2015 6:56 AMPost by BRAD POOLE on March 29, 2015In example 11.  Does it mater what order you set up Fnet?  You wrote Fnet = T2 cos60 - T1  but can you write it as T1 - T2 cos 60?  Your just trying to find the net so it shouldn't mater right?  Thanks.

### Newton's Second & Third Laws of Motion

• Newton’s 2nd Law of Motion: The acceleration of an object is directly proportional to the force applied to the object and inversely proportional to the object’s inertial mass.
• Newton’s 3rd Law of Motion: All forces come in pairs. The force of object one on object two is equal in magnitude and opposite in direction to the force of object two on object one.

### Newton's Second & Third Laws of Motion

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Objectives 0:09
• Newton's 2nd Law of Motion 0:36
• Newton's 2nd Law of Motion
• Applying Newton's 2nd Law 1:12
• Step 1
• Step 2
• Step 3
• Step 4
• Example I: Block on a Surface 1:42
• Example II: Concurrent Forces 2:42
• Mass vs. Weight 4:09
• Mass
• Weight
• Example III: Mass vs. Weight 4:45
• Example IV: Translational Equilibrium 6:43
• Example V: Translational Equilibrium 8:23
• Example VI: Determining Acceleration 10:13
• Example VII: Stopping a Baseball 12:38
• Example VIII: Steel Beams 14:11
• Example IX: Tension Between Blocks 17:03
• Example X: Banked Curves 18:57
• Example XI: Tension in Cords 24:03
• Example XII: Graphical Interpretation 27:13
• Example XIII: Force from Velocity 28:12
• Newton's 3rd Law 29:16
• Newton's 3rd Law
• Examples - Newton's 3rd Law 30:01
• Examples - Newton's 3rd Law
• Action-Reaction Pairs 30:40
• Girl Kicking Soccer Ball
• Rocket Ship in Space
• Gravity on You
• Example XIV: Force of Gravity 32:11
• Example XV: Sailboat 32:38
• Example XVI: Hammer and Nail 33:18
• Example XVII: Net Force 33:47

### Transcription: Newton's Second & Third Laws of Motion

Hello, everyone, and welcome back to www.educator.com.0000

I am Dan Fullerton and in this lesson we are going to talk about Newton’s s and third laws of motion.0004

Our objective is to understand the relation between the force that acts on an object and the objects acceleration.0009

Perhaps, the most important part of the entire course.0015

Write down and utilize vector equations resulting from the applications of Newton's second law.0018

Applying it in third law and analyzing the forces between two objects.0025

Solve problems in which application of Newton's laws leads to simultaneous linear equations.0029

Let us start off by talking about Newton's s law of motion that is so useful in the course.0036

It says the acceleration of an object is in the direction of indirectly proportional to the net force applied and inversely proportional to the objects mass.0042

It is valid only in inertial reference frames.0052

However, for the purposes of this course we are assuming everything we deal with is an inertial reference frame.0055

The way we write it the net force or if you prefer the sum of all forces on an object is equal the mass × acceleration that = ma.0062

How do we apply it?0072

We start off with free body diagrams like we talk in our last lesson.0074

Then, for any forces that do not line up with the x or y axis we break those in the components that do lie on the x or y axis with those pseudo free body diagrams.0079

Then, we write expressions for the net force in the x and y directions and set the net force = mass × acceleration since Newton's law s law tells us f = ma.0088

Finally, solve the resulting equations.0098

We will do lots of examples.0100

Let us start off with a block on the surface.0102

Two forces f1 to the left and f2 to the right are applied to a block on the frictionless horizontal surface as shown.0106

If the magnitude of the blocks acceleration is 2 m/s² find the mass of the block.0112

Since you get a bigger force to the left let us call to the left our x direction here.0119

If we look our net force in the x direction we have 12 in the positive direction - we have 2 in the negative x direction = mass × the acceleration in the x direction.0126

12 -2 is 10 N must equal our mass × acceleration 2 m/s².0141

Therefore, our mass must be 10 N / 2 m/s² or 5 kg.0149

Nice and straightforward.0160

How about if we have some concurrent forces?0162

A 25 N horizontal force northward in the 35 N horizontal for southward at concurrently at a 15 kg object on a frictionless surface.0165

What is the magnitude of the objects acceleration?0175

Let us draw that.0178

We have got 25 N to the north, we have 35 N that is our object.0179

35 N south what is the magnitude of the objects acceleration?0190

Why do not we call it down or south our y direction since we can see that is the bigger force.0200

I am going to write that the net force in the y direction is 35 N -25 N because that points in the -y direction and0207

that must be equal to mass × acceleration in the y direction or 10 N = 15 kg mass × acceleration.0218

Or acceleration then is equal to 10 N / 15 kg which is 0.67 m/s².0232

That is Newton’s second law.0246

As we talk about Newton’s second law an opportune time to talk about mass vs. weight.0249

If you recall mass is a measurement of an object’s inertia.0254

It tells you how much stuff something is made up of.0257

It is a constant.0259

Your mass should be the same unless somebody comes over and starts chopping off limbs and other things that are unpleasant.0261

Weight is the force of gravity on an object.0269

Weight which we write as mg can vary with gravitational field strength.0272

Your weight on earth would be different than your weight on the moon.0276

Your mass however would be the same.0281

Let us do an example with mass vs. Weight.0286

An astronaut weighs 1000 N on earth what is the weight of the astronaut on planet X where the gravitational field strength mg is 6 m/s².0289

Let us figure out the astronauts mass first.0299

The weight of the astronaut mg is 1000 N and therefore mass must be 1000 N / 10 m/s² here on earth or 100 kg.0304

On this planet X, however, the weight is m × gravitational field strength.0319

Let us call that g sub x for g on planet X which is 100 kg mass does not change × 6 m/s² or 600 N.0325

An alien on planet X weighs 400 N what is the mass of the alien?0341

The weight of the alien mg x is 400 N therefore the mass is 400 N ÷ gx which is 6 m/s² or 66.7 kg.0347

What does this have to do with Newton’s second law?0370

Here is the rule.0372

We have been writing Newton’s second law f = MA.0374

We have been writing the force of gravity the weight of an object as mg.0379

Force of gravity is just a specific type of force is mass × we called g the acceleration due to gravity.0384

Writing weight is mg is just an interpretation of Newton’s second law.0391

To shorthand that and we have been using the same step.0397

Already taking into account that we understand Newton’s second law.0399

Let us look at a translational equilibrium problem.0404

In the diagram a 20 N force due north and the 29 N due east act concurrently on an object in the same place of the same time.0407

What additional force is required to bring the object and equilibrium?0416

We need to have one force that is going to balance these two.0420

The way I do this is the first thing I'm going to do is figure out what the resultant of these two are.0424

Let us add them together to see what their net force would be.0430

If we got 20 N to the right and 20 N up I am going to line those up tip to tail so I can add them.0433

I am going to take this 20 N north and I'm going to move it here to the right to remember0439

we can slide vectors as long as we do not change their direction or length.0444

And then to find the resultant I will draw a line from the starting point in the first to the ending point of the last.0449

And I can use the Pythagorean Theorem to figure out its magnitude.0455

That will be the √20² + 20² which is about 28 N.0460

Right now we have the equivalent of a 28 N force NE 45°.0467

What force would be required to bring that in the equilibrium?0473

We have the exact opposite force.0475

We will start a force at the same point and have it go 28 N and down into the left.0478

What we call this force the force that required to bring an object in the equilibrium is known as the equilibrant.0487

Our answer would be 28 N southwest.0497

Another translational equilibrium problem.0503

A 3 N force in the 4 N force acting concurrently on a point.0506

Which force could not produce equilibrium with these forces?0510

Now let us see.0514

The 1 N force produce equilibrium with these.0515

We have a 3 N force, we have a 4 N force and have it go to the left.0518

It looks like the addition of a 1 N force could completely balance those out.0527

We get back to our starting point.0533

1 would work that could produce equilibrium.0535

I think 7 could work too.0539

Let us take a look if we have 3 N and now we line up the 4 N force there.0541

A 7 N force could bring this back to our starting point 7 N in the equilibrant that cannot be the answer.0546

However, there is no way that we can have a 3 N force if 1 N force and no matter what we do with the 9 N force,0555

no matter where we put it there is no way we get back to where we start where we get no net force.0565

It is going to be 9 N force, that is not going to work.0569

You may be wondering how you would do that with the 4 N force?0573

That would work 3 N probably something like that.0576

4 N and you can make a triangle out of it and you can get back to where you started.0583

But 9 N cannot produce equilibrium with a 3 and 4 N force.0588

A way you can test that is add up the 2 forces 3 + 4 = 7 and subtract the two forces.0593

4 -3 is 1.0601

Only forces that are between 1 and 7 could produce equilibrium with that.0602

Anything outside of that range not going to work.0607

Problem here we have got a 15 kg wagon pulled to the right across a surface by a tension of 100 N an angle of 30° above the horizontal.0615

A frictional force of 20 N to the left axis simultaneously.0623

What is the acceleration of the wagon?0627

Let us start off by drawing a free body diagram.0630

Let us get back to those.0632

Especially as our problems start to get a little more complex.0635

And as we look here it is pulled across the surface by a tension of 100 N and an angle of 30° above the horizontal.0644

There is 100 N an angle of 30°.0653

A frictional force of 20 N x to the left.0657

There is our frictional force.0662

What is the acceleration of the wagon?0665

Let us do our next step and break that 100 N force up into its components with a pseudo free body diagram.0668

We will draw our axis again.0679

We still have force of friction to the left the x component of our 100 N is going to be 100 cos 30.0686

That is going to be 100 cos 30 is 86.6 N.0696

In the y direction, we are going to have 100 sin 30 the y component which would be 50 N.0703

We can go to our Newton’s second law equation net force in the x direction is equal to0713

we have 86.6 N to the right - our force of friction which it tells us is 20 N to the left0721

and all of that must be equal to our mass × acceleration in the x direction.0729

Acceleration in the x is 86.6 -20 or 66.6 N ÷ our mass 15 kg which is about 4.44 m/s².0736

Alright, let us take a look at baseball problem.0757

A 0.15 kg baseball moving at 20 m/s is stopped by a player in 0.01 s.0761

What is the average force stopping the ball?0767

We are going to learn some other ways we can solve this two here in a few lessons.0770

But for now let us start by finding its acceleration.0773

Its acceleration is its change in velocity ÷ time which is its final velocity - its initial velocity ÷ time.0777

We can use our kinematic equations because it is a constant acceleration.0785

It is going to be 0 - 20 m/s / 0.01 s or -2000 m/s².0790

What is the negative mean?0802

We are calling its initial velocity positive so this means it is in the opposite direction of its initial velocity.0804

It is slowing down.0810

If we want to know the force, the force is going to be mass × acceleration with Newton’s second law0813

is going to be our mass 0.15 kg × acceleration -2000 m/s² or -300 N.0821

And again, all that negative means it is in the direction opposite what we called positive the direction the ball is going initially.0835

The force in the acceleration are always going to be in the same direction so they are both negative by Newton’s second law.0842

Let us take a look at some steel beams.0850

A steel beam of mass 100 kg is attached by cable to a 200 kg beam above it.0854

The two were raised upward with an acceleration of 1 m/s² by another cable attached to the top beam.0860

If we assume the cables are mass less find the tension in each cable.0866

Let us start.0870

We will call this a y direction and we will analyze beam 1 first.0872

Here is our free body diagram for beam 1.0878

We have tension 1 pulling up on it, we have tension 2 pulling down on it and we have its mass m1 g down.0880

There is beam 1.0892

We did the same thing with beam 2.0895

We will draw a dot for our object.0898

We have T2 pulling it up and only its weight m2 g pulling it down.0899

Let us take a look at applying Newton’s second law here.0906

For beam 1 write the net force in the y direction is equal to we have T1 - T2 – m1 g and all of that =m1 a or we could write that T1 = T2 + m1 g + m1 a.0909

Let us go down and will start here on number 2.0938

Net force in the y direction for 2 is going to be T2 – m2 g and that has to equal m2 a, Newton’s second law or T2 is going to be equal to m2 × g + a.0943

Since we know those we can solve right away that is going to be equal to m2 which is 100 kg × g10 + a1 or 11 m/s².0961

T2 = 1100 N.0975

We can come back to beam 1 where T1 = T2 + m1 + m1 a0980

T1 = T2 1100 N + we have m1 g 200 × 10 + m1 a 200 × 10989

So T1 therefore = 2000 + 200 + 1100 is 3300 N.1006

There are the tensions in our cables.1017

Let us take a look at another one here.1022

The system below is accelerated by applying a tension T1 to the right most cable,1025

Assuming the system is frictionless determine the tension T2 in terms of T1.1030

You can do this in a very detailed way or we can use a little bit of systems thinking to try and make it nice and simple.1035

The first thing I'm going to look at is I’m going to take a look and say you know what if all of these we consider one object for the moment.1042

We have T1 applying a force on that entire object.1050

We could write that T1 the net force on that big object is the total mass 7 × the acceleration a or a = T1 / 7.1054

If we come over here and we look at just of this block is an object is a 2 kg block there is our free body diagram.1069

We got a normal force, its weight, I will call this m2 I suppose and T2 acting on it.1079

The only unbalanced force is going to be T2.1088

Normal force and its weight have to exactly balance otherwise it spontaneously accelerate up off the table or go through it neither of which happen.1090

Looking in the x direction at f net x = MA x or T2 = m2 which is 2 kg × ax1100

If T2 = 2a and a= T1 / 7 T2 must equal 2 × a T1 / 71113

T2 = 2 / 7 T1.1126

Taking a look at some banked curves.1137

Curves can be banked at just the right angle that vehicles traveling a specific speed can stay on the road with no friction required.1140

It is very important if you live somewhere like I do where there is lots of ice and the snow on the roads in the winter.1146

Given a radius for the curve in a specific velocity at what angle should the bank of the curve be built.1152

Let us start by drawing a free body diagram for our system.1159

There is our y, there is our x.1164

Our object are car even though it is going to be on an incline of some sort, is not moving in the direction that inclined.1170

We are not going to tilt our axis here.1177

Before we draw our object let us say we put our angle of our ramp.1181

Let us make it really steep and dramatic here.1185

Let us have it look something like that.1189

There is the angle of our road just as a reference.1190

We will call this angle θ which means that if we draw on normal to it, a normal force on our car this would also be θ.1194

Here is our normal force.1210

Here is the weight of our object of our car mg.1212

Or if we want to do our pseudo free body diagram let us do that right beside it.1217

If we break that up in the components we still have mg straight down.1233

The normal force if we want the horizontal component that is going to be the adjacent.1239

As I look at this angle the x component is going to be the opposite side in this case.1245

That is going to be n sin θ here and the vertical piece is a side that right beside the angle that adjacent to it.1252

This piece is going to be n cos θ.1263

Let us write our Newton’s second law equations.1268

Net force we will look at the x direction first is also going to be what is causing the centripetal force as it goes around a circle.1273

That is what is causing the centripetal force to allow it to move in a circle to go around a curve of some1282

radius is going to be the horizontal component of the normal force n sin θ.1286

F net x which is also the net centripetal force is n sin θ which is ma by Newton’s second law.1294

Since it is a centripetal acceleration moving in a curve, in a circle, we could write that as mv² / r.1304

We will call that equation 1.1312

Analyzing in the y direction, net force in the y direction we have n cos θ - mg and1315

that has to be equal to 0 because there is no acceleration vertically.1325

Therefore we can say that n must be equal to mg / cos θ.1329

We will call that our second equation.1336

Now to start to solve this let us see if we can combine equations 1 and 2 to write n sin θ = mv² / r we will start with 1.1340

But we now know that n = mg / cos θ.1359

This implies then that we still have a sin θ.1366

We have an mg from our n up here ÷ cos θ must be equal to mv²/ r.1373

On the left inside there, sin/ cos is the tan function so we have mg tan θ = mv² / r.1392

I can divide a mass of both sides to say that g tan θ = V² / r.1406

Or θ if we want the angle is going to be the inverse tan of V² / gr.1415

If we know the speed we want the vehicles to travel on that curve.1428

We know the radius of the curve.1432

We can determine exactly what angle we should build that curve at so that the cars do not require a whole lot of friction on the road.1435

Taking a look at tension in cords.1445

Determine the tensions T1 and T2 in cables holding a 10 N weight stationary.1447

As we look at this first thing I think I am going to do again is draw a free body diagram for my object.1454

We will start to draw our axis here and I will draw the one for the pseudo free body diagram too1461

because I can already see am going to have a force and angle.1470

We will draw our x, that should do.1475

Starting with the free body diagram there is our object.1484

We have its weight which is given to us.1489

It is not telling us it is mass when it says it is 10 N.1491

That is its weight so we have 10 N down.1494

We have tension T1 strings cords can only pull so that must be our T1.1497

We have a T2 an angle of 60°.1505

I'm going to do my pseudo free body diagram breaking up T2 into its components.1512

I still have 10 N down.1517

T1 to the left.1523

The x component of T2 is going to be T2 cos 60°.1525

We have T2 cos 60° here in the y component is going to be T2 sin 60°.1532

I can start writing my Newton’s second law equations.1542

Net force in the x direction is going to be we have T2 cos 60 - T1 and all of that is going to have to be equal to 0.1547

There is no acceleration it is sitting there in equilibrium which implies then that T1 is going to be equal to T2 cos 60°.1563

Let us take a look at the y now.1577

Net force in the y direction is going to be T2 sin 60° -10 N.1580

Again, that has to be equal to 0.1594

Therefore, T2 must equal 10 Newton’s / sin 60° which is 11.5 N.1598

There is T2.1608

I can put that into my equation for T1.1611

Therefore T1 = 11.5 cos 60° or 5.77 N.1615

We found the tension in our two cables there.1628

Looking at this from a graphical perspective we will take an example where the velocity of1633

an airplane in flight is shown as a function of time T in the graph.1637

Velocity time.1641

At which time is the force exerted by the plane's engines on the plane the greatest?1643

The way I think about this one is we are going to have the greatest force when we have the greatest acceleration.1649

We flee on the big force we need a big acceleration and since acceleration I should say force is proportional to acceleration.1655

Acceleration is the slope or the derivative of the velocity time graph.1665

Where do we have the biggest slope?1670

It is probably occurring somewhere right around there which if I draw that down is right around 4.5 s.1672

We have the greatest slope at around 4.5 s that must be the time that which we have the greatest force.1683

Given the graph of velocity vs time for the particle shown below where V is proportional to T²1695

sketch a graph of the net force exerted on the object as a function of time.1701

If V is changing that way acceleration is the derivative of velocity.1707

We start off with 0 slope if I wanted to put acceleration on the same graph in red we start off at 0 acceleration.1712

As we go along we are going to have higher and higher, larger and larger amounts of acceleration.1720

It looks like our acceleration graph is probably going to be linear something of this shape.1726

If we have that shape for acceleration we have to have the same shape for our force time graph since force = mass × acceleration.1736

So I would draw our force graph with the shape like that when you are increasing up to the right.1746

Newton’s third law this is a pretty cool one as well.1757

All forces come in pairs, you never have just a single force, they are always pairs.1760

If object 1 exerts a force on object 2, object 2 exerts a force of equal magnitude but opposite in direction back on object 1.1765

Or if you wrote it mathematically the force of object 1 on object 2 is equal in magnitude but opposite in direction to the force of 2 on 1.1775

I should note that those are vectors of course, Newton’s third law.1785

If I punch you in the nose with a force of 100 N, your nose punches my fist with a force of 100 N back in the opposite direction.1790

Alright, some examples.1802

How does a cat run forward if the cat runs forward does not it push backwards on the ground?1803

It is the ground actually propels the cat forward?1810

Or if you want to swim forward which way do you push the water?1813

You push backward on the water applying a force on the water and the water’s reactionary force by Newton’s third law is what pushes you forward.1817

Or if you want to jump in the air which way do you push with your legs?1825

Do not you push down on the ground as hard as you can as quickly as you can?1828

You push down on the ground it is the opposite force of the ground pushing up on you that propels you up into the air.1832

When we have these two forces from different objects we call those action reaction pairs.1843

If a girl is kicking a soccer ball let us identify some of those pairs.1847

We have the force of the girl’s foot on the ball and the ball is actually applying a force back on the girl’s foot or a rocket ship in space.1851

The rocket ship is propelled by pushing gases out.1866

The reactionary force is that those gases push the rocket causing the acceleration.1874

How about gravity on you? gravity on me?1884

Right now the Earth's gravity is pulling me down.1887

Guess what though, I'm pulling the earth upward with the exact same force.1894

How come I have such a more dramatic effect?1904

If I jump off a cliff, I'm being pulled down toward the earth with the same force I'm pulling the earth up toward me,1906

why does it look like it is going to hurt the earth nearly as much as me?1913

I'm going to accelerate a lot more because for the same force I have a much smaller mass.1916

That same force applied to the Earth's huge mass gives a very little almost an immeasurable acceleration.1922

Earth's mass is approximately 81 × the mass of the moon.1933

If Earth exerts a gravitational force of magnitude f on the moon, the magnitude of the gravitational force of the moon on Earth is.1937

It is a straightforward application of Newton’s third law.1944

If the Earth is pulling on the moon with force f, the moon must pull on the earth with force f.1948

Forces come in pairs that are equal and opposite.1953

Or the sailboat question.1958

A 400 little girl standing on a dock exerts a force of 100 N on the 10,000 N sailboat as she pushes it away from the dock.1961

How much force does the sailboat exert on the girl?1970

In order to know the force the sailboat exerts on the girl we need to find the force that the girl exert on the sailboat.1973

She exerts a force of 100 N on the sailboat, the sailboat must have that exact same magnitude of force back on her.1980

This 10,000 N here that is just describing the weight of the sailboat not talking about the interaction of the girl and the sailboat.1987

Alright and another one, hammer and nail.1997

A carpenter hits the nail with a hammer, compare to the magnitude of the force the hammer exerts on the nail.2001

The magnitude of the force the nail inserts on the hammer during contact is the exact same.2006

Why does the nail get propelled forward and the hammer not so much different?2015

The nail has a much smaller mass.2019

And our last question here.2026

If force is only come in pairs that are equal and opposite why do not all forces cancel each other?2028

The trick is these forces act on different objects.2034

They all act on the same object they would cancel out but if they do not they are acting on different objects.2042

Think about it in terms of free body diagram to be doing a free body diagram for each of these objects.2048

You are not going to have a free body diagram that has the initial force in the reactionary force or the paired force all on the same diagram.2053

You may have heard Newton’s third law stated as for every action there is an equal and opposite reaction.2065

Which is something of a restatement of the law but it also can be somewhat confusing2070

because you are not really talking about what actions and reactions are.2075

Instead, Newton’s third law the force of object 1 and object 2 is equal in magnitude and opposite direction to the force of object 2 on object 1.2078

Forces only come in pairs, you can never have a singular force.2088

Thank you for watching www.educator.com.2093

We will see you again real soon and make it a great day everybody.2104

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