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Dan Fullerton

Dan Fullerton

1998 AP Practice Exam: Multiple Choice

Slide Duration:

Table of Contents

I. Introduction
What is Physics?

7m 12s

Intro
0:00
Objectives
0:11
What is Physics?
0:27
Why?
0:50
Physics Answers the 'Why' Question
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
Graphical Vector Addition
2:54
Graphical Vector Addition
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
II. 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
Example XV: Quadratic Solution
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
Radians and Degrees
0:32
Degrees
0:35
Radians
0:40
Example I: Radians and Degrees
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
III. 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
IV. 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
V. 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
VI. 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
VII. Rotational Motion
Rotational Kinematics

32m 52s

Intro
0:00
Objectives
0:07
Radians and Degrees
0:35
Once Around a Circle: In Degrees
0:36
Once Around a Circle: In Radians
0:48
Measurement of Radian
0:51
Example I: Radian and Degrees
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
VIII. 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
IX. 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
X. 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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Lecture Comments (14)

1 answer

Last reply by: Professor Dan Fullerton
Sat May 6, 2017 5:28 PM

Post by Woong Ryeol Yoo on May 6, 2017

Hi mr. Fullerton.
Is the equation sheet given for the Multiple Choice on both the AP physics c exams?
I know the past exams only gave table of information for the MCs. Does the current exam give equation sheet and table of information for the MCs?

1 answer

Last reply by: Professor Dan Fullerton
Thu Mar 23, 2017 5:17 AM

Post by Woong Ryeol Yoo on March 22, 2017

Hi Mr. Fullerton.
So I only missed two questions in the 1998 released exam. But I was wondering if this exam is outdated in terms of the problem style and contents. Is the current c mech exam way different than the 1998 exam? Is it more difficult now?

1 answer

Last reply by: Professor Dan Fullerton
Tue Dec 20, 2016 6:14 AM

Post by Simon Fei on December 19, 2016

How did you get the formula |a|=omega^2*A for number 29?

1 answer

Last reply by: Professor Dan Fullerton
Sun Sep 18, 2016 7:08 AM

Post by Shive Gowda on September 18, 2016

I could not find the book.

1 answer

Last reply by: Professor Dan Fullerton
Sat Apr 25, 2015 5:04 PM

Post by Micheal Bingham on April 24, 2015

For number 7 why isn't the gravitational force constant on the asteroid, like on Earth?

3 answers

Last reply by: Professor Dan Fullerton
Thu Mar 17, 2016 5:55 AM

Post by Dianfan Zhang on March 27, 2015

Where are the links for this 1998 practice exam? The links from google seem to be different exams. Thanks

1998 AP Practice Exam: Multiple Choice

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
  • 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

Transcription: 1998 AP Practice Exam: Multiple Choice

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

I’m Dan Fullerton and in this lesson we are going to take an old AP practice exam and walk through it step by step.0004

We are going to start with a multiple choice portion of the test.0010

You can find it with the www.google.com search or from the AP Physics site.0014

The links are down below as well.0018

We are just going through the multiple choices one by one.0020

Take a minute, give it a try, and come back here and we will see how you did as we walk through each of the problems.0023

Starting with the number 1, we have got a force exerted by a broom handle on a mass at some angle, the work done is what?0031

This is just the definition of work, force × displacement × cos of the angle between them and that looks like answer B.0040

Number 2, we have got a projectile launched with the horizontal component and vertical component of velocity, no air resistance,0053

and when it is at its highest point what do we know about the vertical velocity, horizontal velocity, and vertical acceleration?0060

Its highest point, the vertical velocity is going to be 0.0067

We know the horizontal velocity is not going to change, it is going to remain constant.0072

Our vertical acceleration, the entire time it is in the air is just g.0076

It looks like our answer there must be E.0081

Taking a look at number 3, here we have a graph showing the velocity as a function of time for an object moving in a straight line,0087

find the corresponding graph that shows displacement as a function of time.0095

The trick here is realizing that displacement is the area under the VT graph or if we look at the position time graph, the slope of that should give you velocity.0101

To me, the only graph that it looks like it comes even close there is going to be D.0112

Number 4, position of a toy locomotive is given by x = T³ -6 T² + 9 T and we want to find the net force.0121

In right away, I’m thinking if we want net force, let us find acceleration and multiply that by the mass.0137

If we are given position, velocity which is X prime, the first derivative that is going to be 3 T² -12 T + 9,0143

so acceleration which is the second derivative of velocity or the second derivative of position or the first derivative of velocity is just going to be 6T-12.0152

We are looking the net force on locomotive is equal to 0 when T is equal to, for that to be the case, our acceleration has to be 0, that means 6T-12 equal 0.0164

6T must equal 12 or T = 2s, so 2s is the answer D.0178

Number 5, we have a system of wheels fix to each other free to rotate about a frictionless axis, four forces are exerted on the rims of the wheels, find the net torque.0189

The net torque, we just add those forces × their displacements, making sure we take into account their direction.0200

It looks like on all of these, the sign of the angle sin θ that is going to be 90° so 1.0207

Our net torque, we have from top to bottom, we have -2 F × 3 R, negative because it is causing a clockwise rotation.0213

We have then + F × 3 R /on the left, we have + F × 2 R and we have + F × R 3.0224

When I put that all together, I have -6 FR + 8 FR, for a net torque of 2 FR and our answer is C.0244

Looking at number 6, the wheel of mass M and radius r, rolls on a level surface without slipping.0260

If the angular velocity of the wheel is ω what is its linear momentum?0268

If V = ω r and we know p=MV, that is just going to be M ω r.0272

Now that is easy, the answer is A.0283

Let us take a look at number 7, 7 and 8 refer to the same situation.0288

A ball tossed straight up from the surface of a small spherical asteroid with no atmosphere.0294

It rises to a height equal to the asteroid’s radius and then fall straight down towards the surface of the earth.0301

What forces act on the ball on its way up?0305

The only force it is going to act on it is going to be gravity pulling it down and that is going to decrease the higher the ball gets, so the answer has to be A.0309

And number 8, the acceleration of the ball at the top of its path is?0320

The acceleration is going to be ¼ what it was when it was on the surface due to the inverse square law?0325

That is going to have to be answer is D, it looks like.0332

There is 7 and 8, let us move on and take a look at number 9.0336

The equation of motion of the simple harmonica oscillator is d² x / dt² = -9x, find the period of oscillation.0343

Let us write this first in our standard differential equations form, d² x / dt² + 9x = 0.0354

And remember, that value right there is what we call ω².0364

If ω² = 9 then ω must equal 3 and period is 2π / ω which is going to be 2π / 3.0369

We will see if that is one of our answers, yes that is D.0381

There we go, taking a look at number 10.0385

A pendulum with a period of 1s on earth with the acceleration due to gravity is G, is taken to another planet where its period is 2 s.0391

The acceleration due to gravity on the other planet is most nearly, on earth we know the period on any planet at 2 π √L /G.0399

As we look at that, on the new planet its period goes to 2s which means we must have 1/4 gravity because0413

we have this inverse square root relationship because it is proportional to √L /G must be ¼ G in order to double the period.0422

The answer has to be a, G/4.0432

You can work that out mathematically as well with all the details and numbers if you want to.0437

Number 11, a satellite of mass M moves in the circular orbit of radius r with constant speed V, which of these statements are true?0444

Its angular speed is V /r, angular speed is V/r, that is one of our definitions, one is true.0454

Its tangential acceleration is 0, of course it is moving at a constant speed so 2 is true.0463

Let us see, the magnitude of it centripetal accelerations is constant, AC = V² /R, V is not changing, r is not changing,0471

so that has to be constant, so 3 is true.0481

All 3 of those, E must be the right answer.0484

Number 12, we have a graph of force vs. Time and for the time interval from 0 to 4 s, the total change of momentum is?0491

For number 12, change in momentum impulse is the area under the force time graph and our total area under the graph there is 0.0502

Therefore, the answer has to be C.0511

Taking a look at 13, we have a disk of mass M moving horizontally to the right with some speed V.0516

It is going to collide with a disk of mass 2 M moving with b/2, find the speed after the collision.0524

That looks like a conservation momentum problem where initial momentum we have MV + 2 M × V / 20531

which is going to be equal to our total combined mass 3 M times some unknown velocity V prime.0540

MV + MV 2 MV = 3 MV prime or V prime is just going to be equal to 2 V /3 and that is the answer C.0548

On the 14, 14 and 15 both refer to this object attached to a spring, moving in a circle, what is the centripetal force on the disk?0562

That we can get from Hooke’s law, that force is going to be jx which is 100 N/m × the displacement0574

from its equilibrium our happy position, 0.03 m is just going to be 3 N, answer B.0582

What is the work done on the disk by the spring during one full circle?0593

There is a trick question, the force is being applied towards the center of the circle but the displacement is always tangent to that, perpendicular to that at 90°.0599

The work done in this case is going to be 0.0610

For 15, we can state that A must be the right answer.0613

Moving on to 16 here, 16 and 17 refer to this graph.0621

If a particle was released from rest, the position are 0, its peak position toward 0 is most nearly.0629

That looks like a conservation of energy problem where our initial potential + our initial kinetic energy must equal our final potential + final kinetic energy.0635

And our initial potential energy when we are at our 0 is 3u 0 must equal, at 2r 0 our potential is u 0 + whatever energies left must be our final kinetic energy.0647

Therefore, final kinetic energy must be 2 u0 and kinetic energy is ½ MV².0663

Solving this, MV² must equal 4u 0 and therefore, V² must equal 4u 0 /M or V = √4u 0/M and that looks like answer is C.0670

Let us take a look at 17, if the potential energy function is given by that equation which of the following is an expression for the force?0693

Force is the opposite of the derivative of the function along that path r which is going to be - the derivative with respect to0704

r of our function VR to the -3/2 + C which is going to be, we can pull the B out of there is a constant that will be -2 B × our derivative0713

which will be -3/2 r⁻⁵/2 which implies then that our force is going to be equal to, our negative will cancel out and I will have 3 B /2 r⁻⁵/2,0726

which looks like that is going to be answer A.0743

Moving on to 18, we have got a frictionless pendulum of length 3m swinging with an amplitude of 10° so we can use that small angle approximation it is under about 15.0749

Its maximum displacement, the potential energy is 10 joules, what is the kinetic energy when its potential energy is 5 joules?0761

Energy is conserved that is going to be 5 joules, answer B, 5 + 5 = 10.0772

Alright 19, we have got a descending elevator, a 1000 kg, uniformly accelerate to rest over a distance of 8 m and tell us the tension in the cable.0782

The speed Vi of the elevator at the beginning is most nearly what?0792

We can start by finding the acceleration by using a free body diagram.0796

Tension up it tells us is 11,000 N we will call down the positive y direction and we have the weight of the elevator, MG which is going to be 10,000 N.0802

The net force in the y direction must be -1000 N and that must be equal to our mass × our acceleration.0813

Our mass is 1000, therefore, the acceleration must be just -1 m /s².0822

It becomes a kinetics problem, we are trying to find V initial, V final = 0, Δ y is 8m, and the acceleration in the y is -1 m /s².0829

We could use V final² = V initial² + 2a Δ y or V initial² = V final² -2a Δ y, substitute in for our values, VF² that will be 0² -2 × -1 × 8m.0842

Vi² = 6 T m² / s², Vi is square root of that which is 4 m /s, which is the answer A, so there is 19.0863

Taking a look here at 20, two identical stars at fix distance D apart, revolve at the circle about their center of mass.0881

Each star has a mass M, speed V, which is a cracked relationship among those quantities?0890

As I look at 20 here, if they are revolving around each other, they are moving in the circular path, the net centripetal force is MV² /r,0897

which implies then that G × the mass of the first × the mass of the second divided by the square of the distance between them must equal MV² /r is D /2,0907

the circular path which implies with a little manipulation that V² = GM × M × D /D² × 2 M.0922

Or solving for V² that is GM /2 D which is answer was B.0936

On 21, block of mass M is accelerated across a rough surface by a force of magnitude F exerted an angle 5 with a horizontal.0946

Frictional force has magnitude F, find the acceleration of the block.0959

Let us start with a free body diagram here.0963

We have our normal force up, we have the weight down, we have some applied force F at some angle of I, and we have a frictional force.0966

The net force in the x direction is going to be F cos I, the component of F along the x - F is equal the MA,0979

which implies that the acceleration must be F cos i - the frictional force divided by the mass which looks like that is answer D.0990

And 22, what is the coefficient of friction between the block and the surface?1005

To do that, let us start looking in the y direction.1009

Net force in the y direction is going to be M + F sin i - MG all equal to 0 because it is not accelerating in the y direction,1012

which implies that the normal force = MG - F sin i.1023

The frictional force, friction is fun so that is μ × the normal force which implies that the coefficient of friction μ is our frictional force / normal force1030

is going to be our frictional force / our normal force we said was MG – F sin i.1041

It looks like that answer E.1050

Alright, 23, was a problem that they skipped on the exam.1058

There is either a problem with the question or the solution, something did not come out right.1062

We will skip that one and move on to 24.1066

Alright, 2 people are initially standing still on frictionless ice, they push on each other so that one person of mass 120 kg moves to left at 2 m /s.1077

The other person mass 80 kg moves to the right at 3 m /s, what is the velocity of the center of mass?1086

Another trick question, the initial velocity of the center of mass is 0 and there no external forces.1093

The final velocity of the center of mass must be 0, the answer there must be A.1099

Moving on to 25, for 25 here, we have a figure of a dancer on a music box moving counterclockwise at constant speed,1108

which of those graphs best represents the magnitude of the dancer’s acceleration as a function of time during one trip around beginning at point P?1121

It begins from point P, from P to Q there is no acceleration and from R to S there is no acceleration.1131

And from Q to R, during those current parts the acceleration is constant AC = V² / r.1137

I think we are looking for something that looks like B.1144

26, at target T lies flat on the ground 3 m from the side of a building that is 10 m tall.1150

Student rolls a ball off the horizontal roof and the direction of the target.1158

The horizontal speed of which the ball must leave the roof distract the target is most nearly what?1162

Let us first figure out how long it is going to take in order to hit the ground.1168

We have done that many times now, that is a vertical problem, where Vi vertically is 0 or call down positive y.1173

V final we do not know, Δ y is 10 m, AY 10 m /s² and T is what we are trying to find.1182

Δ y = V initial T + ½ AYT² and since V initial is 0, that term goes away.1192

Δ y = ½ AYT² or T = 2 Δ y / √ay which is going to be 2 × 10 m / 10 m /s² square root which is just going to be √2s.1204

The horizontal analysis, we know that Δ x needs to be 3 m.1225

We know our time is √2s, so the velocity in the x direction is just Δ x / t which is 3m /√2s, 3m /√ 2s, for number 26 looks like the answer must be C.1232

And 27, to stretch a certain nonlinear spring by an amount, x requires that force, what is the change in potential energy when it stretch 2 m from its equilibrium position?1257

We need to find the amount of work done in stretching the spring from 0 to 2 m and the work done will be the potential energy stored in that spring.1268

Our potential energy will be the integral from x = 0 to 2 m of FX DX which is the integral from 0 to 2.1279

Our force is 40x-6 x² Dx, so that is going to be 40x² / 2 -6x³/ 3 all evaluated from 0 to 2, which is going to be,1290

let us simplify this first, 20 x² -2x³ evaluated from 0 to 2, which will be 20 × 2² -2 × 2³ -0 -0 is going to be 20 × 2² that is going to be 80 - 16 or 64 joules.1306

27 must be D.1335

Alright 28, when the block slide a certain distance down an incline, the work done by gravity is 300 joules.1339

What is the work done by gravity if the block slides the same distance up the incline?1347

That is going to be -300 joules, the answer is C.1351

29, particle moves in the xy plane with coordinates given by x = a cos ω T and Y = a sin ω T, where A is 1½ m and ω is 2 radians /s.1358

What is the particles acceleration?1372

Remember, the magnitude of the acceleration is ω² A which is going to be 2 radians /s² × A 1.5 m is just going to be 6 m/s², answer must be E.1375

Let us take a look here at number 30, for the wheel and axel system shown,1398

which in the following expresses the condition required for the system to be in static equilibrium?1405

For 30, we are looking for all of our torques and our forces has to be balanced.1411

Right away, I can say that M1 G, the force of gravity on block 1 × its distance from our axle A must be equal in magnitude, 2M2 G B.1421

Therefore, AM1 = BM 2, that is going to be answer B.1435

Taking a look here at 31, an object having an initial momentum is represented by that vector above,1448

which in the following sets of vectors represent the momentum of the 2 objects after the collision?1456

The sum of those 2 vectors has to be the exact same of what you have above because you do not have any external forces here .1461

If conservation of linear momentum, that looks like the only vectors that we could add together to get what you have up above there is E.1468

32, a wheel with some rotational inertia mounted on a fix frictionless axle with the angular speed ω is increased from 0 to ω final at time T.1481

What is the net torque required?1490

Net torque is moment of inertia × angular acceleration which is going to be moment of inertia × angular acceleration1492

is the change in angular velocity with respect to time, which is going to be I ω final / T, since ω initial was 0.1502

At 32, it looks like our answer must be E.1514

33, what is the average power input to the wheel during this time interval?1522

Remember, power is force × velocity in a linear world.1527

Rotationally, we can do that same analog.1531

Instead of force, we are going to have torque.1533

Instead of average velocity, we are going to have average angular velocity so that is going to be I ω final / T our torque × average rotational velocity1536

is going to be halfway between the initial and final values because it is a constant angular acceleration or ω final /2, which will give us I ω final² / 2 T, which is answer B.1550

To 34, an object is released from rest to time T = 0 and falls with an acceleration given by a = G – BV, where B is the object’s speed.1571

V is the object’s speed, B is a constant.1583

Our drag force, retarding force question.1584

Which of the following is a possible expression for the speed of the object as an explicit function of time?1588

A = G - BV and we know we can draw the graph to begin with, knowing that our acceleration start at some value G.1593

We are going to have an exponential BK as a function of time.1602

We just have to find which of those functions fits that shape.1607

Initially, a if t is 0, we are going to have V = G × 1 -0 / B, so that is going to be G × 1 ÷ B.1611

We are going to start at the high point and as it gets bigger, we are going to get lower and lower.1625

Right away, A fix that shape.1629

And 35, ideal mass of spring fix to the wall, block of mass M oscillate with amplitude A and maximum speed VM.1636

Find the force constant of the spring.1646

Looking at conservation of energy, ½ KA² the maximum potential energy in the spring must equal ½ MV² its maximum kinetic energy,1650

which implies then that K is going to be equal 2 MV² × 2/2 A² which is just MVM² / a².1662

The correct answer is D.1675

Hopefully that gets you a good feel for where you are strong on the concepts for this test and areas that need a little bit more improvement.1679

Thank you so much for watching www.educator.com.1686

I look forward to seeing you again soon and make it a great day everybody.1688

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