Cartesian and polar coordinates are introduced and how to switch from one to the other is derived. The concept of angular displacement and arc length are demonstrated. Circumference is shown to be an arc length. Want Lecture Notes? This is an AP Physics 1 topic.

Content Times:

0:10 Cartesian coordinates and circular motion

1:00 Polar coordinates and circular motion

1:40 Switching between polar and Cartesian coordinates

2:18 Introduction to Angular Displacement and Arc Length

3:24 The Arc Length equation

4:13 Circumference and Arc Length

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Calculus based review of equations I suggest you memorize for the AP Physics C: Mechanics Exam. Please realize I abhor memorization, however, there are a few equations which I do recommend you memorize. I also list equations NOT to memorize and ones which I suggest you know how to derive. Also a note about Moments of Inertia and the AP Exam.

For the calculus based AP Physics C mechanics exam. Want Lecture Notes?

Content Times:

0:22 Equations to Memorize

2:06 Derivative as an Integral Example

6:52 Equations NOT to memorize

8:10 Equations to know how to derive

10:14 Moments of Inertia and the AP Exam

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Calculus based review of Simple Harmonic Motion (SHM). SHM is defined. A horizontal mass-spring system is analyzed and proven to be in SHM and it’s period is derived. The difference between frequency and angular frequency is shown. The equations and graphs of position, velocity, and acceleration as a function of time are analyzed. the phase constant Phi is explained. And Conservation of Mechanical Energy in SHM is discussed. For the calculus based AP Physics C mechanics exam.

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Content Times:

0:12 Defining simple harmonic motion (SHM)

0:53 Analyzing the horizontal mass-spring system

2:26 Proving a horizontal mass-spring system is in SHM

3:38 Solving for the period of a mass-spring system in SHM

4:39 Are frequency and angular frequency the same thing?

5:16 Position as a function of time in SHM

5:44 Explaining the phase constant Phi

6:19 Deriving velocity as a function of time in SHM

7:33 Deriving acceleration as a function of time in SHM

9:05 Understanding the graphs of position, velocity, and acceleration as a function of time in SHM

12:16 Conservation of Mechanical Energy in SHM

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Calculus based review of Universal Gravitation including Newton’s Universal Law of Gravitation, solving for the acceleration due to gravity in a constant gravitational field, universal gravitational potential energy, graphing universal gravitational potential energy between an object and the Earth, three example problems (binding energy, escape velocity and orbital energy), and Kepler’s three laws. For the calculus based AP Physics C mechanics exam.

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Content Times:

0:10 Newton’s Universal Law of Gravitation

1:52 Solving for the acceleration due to gravity

2:02 Universal Gravitational Potential Energy

4:52 Graph of Universal Gravitational Potential Energy between an object and the Earth

6:09 Binding Energy Example Problem

8:22 Escape Velocity Example Problem

9:54 Orbital Energy Example Problem

12:29 Kepler’s Three Laws

12:54 Kepler’s First Law

14:56 Kepler’s Second Law

15:25 Deriving Kepler’s Third Law

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Calculus based review and comparison of the linear and rotational equations which are in the AP Physics C mechanics curriculum. Topics include: displacement, velocity, acceleration, uniformly accelerated motion, uniformly angularly accelerated motion, mass, momentum of inertia, kinetic energy, Newton’s second law, force, torque, power, and momentum.

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Content Times:

0:12 Displacement

038 Velocity

1:08 Acceleration

1:33 Uniformly Accelerated Motion

2:15 Uniformly Angularly Accelerated Motion

2:34 Mass

3:19 Kinetic Energy

3:44 Newton’s Second Law

4:18 Force and Torque

5:12 Power

5:45 Momentum

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Calculus based review of the cross product torque equation, how to do a unit vector cross product problem, rotational equilibrium, the rotational form of Newton’s second law, the angular momentum of a particle and of a rigid object with shape, the derivation of conservation of angular momentum, and a conservation of angular momentum example problem which reviews a lot of the pieces necessary to understand conservation of angular momentum.

For the calculus based AP Physics C mechanics exam. Want Lecture Notes?

Content Times:

0:15 The cross product torque equation

1:10 Unit vector cross product example problem

3:32 Rotational equilibrium definition

4:55 Rotational form of Newton’s second law

5:37 Angular momentum of a particle

7:08 Angular momentum of a rigid object with shape

7:49 Conservation of angular momentum derivation

8:57 Conservation of angular momentum example problem

10:57 Visualizing the problem

12:04 The conservation of angular momentum equation

12:54 Solving for the constant value of the variable y.

14:04 Substituting in known values

15:38 Does our variable answer make sense?

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Calculus based review of moment of inertia for a system of particles and a rigid object with shape, the derivation of rotational kinetic energy, derivations of the following moments of inertia: Uniform Thin Hoop about is Cylindrical Axis, Uniform Rigid Rod about its Center of Mass and about one end, also the parallel axis theorem, torque, the rotational form of Newton’s Second Law, pulleys with mass and the force of tension, the Right Hand Rule for direction of torque, and rolling with and without slipping.

For the calculus based AP Physics C mechanics exam. Want Lecture Notes?

Content Times:

0:10 Moment of Inertia of a system of particles derivation

1:46 Rotational Kinetic Energy derivation

2:49 Moment of Inertia of a rigid object with shape derivation

3:52 Moment of Inertia of a Uniform Thin Hoop about its Cylindrical Axis derivation

5:31 Moment of Inertia of a Uniform Rigid Rod about its Center of Mass derivation

8:02 Moment of Inertia of a Uniform Rigid Rod about one end derivation

9:16 The Parallel Axis Theorem

11:29 Torque

12:21 Simple torque diagram

14:14 Rotational form of Newton’s Second Law

15:07 Pulleys with mass and the Force of Tension

15:33 The Right Hand Rule the for the direction of torque

16:56 Rolling without Slipping

17:40 Rolling with Slipping

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Calculus based review of instantaneous and average angular velocity and acceleration, uniformly angularly accelerated motion, arc length, the derivation of tangential velocity, the derivation of tangential acceleration, uniform circular motion, centripetal acceleration, centripetal force, non-uniform circular motion, and the derivation of the relationship between angular velocity and period.

For the calculus based AP Physics C mechanics exam.

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Content Times:

0:10 Instantaneous and Average Angular Velocity and Acceleration

1:14 Uniformly Angularly Accelerated Motion

2:16 Arc Length

3:22 Tangential Velocity Derivation

4:29 Tangential Acceleration Derivation

6:03 Uniform Circular Motion and Centripetal Acceleration

8:04 Centripetal Force

9:20 Non-Uniform Circular Motion

10:21 Angular Velocity and Period Relationship Derivation

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Calculus based review of conservation of momentum, the momentum version of Newton’s second law, the Impulse-Momentum Theorem, impulse approximation, impact force, elastic, inelastic and perfectly inelastic collisions, position, velocity and acceleration of the center of mass of a system of particles, center of mass of a rigid object with shape, and volumetric, surface and linear mass densities. For the calculus based AP Physics C mechanics exam.

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Content Times:

0:11 Momentum

0:38 Momentum and Newton’s Second Law

1:44 Conservation of Momentum

2:35 Impulse-Momentum Theorem

4:23 Impulse Approximation and Force of Impact

5:32 Elastic, Inelastic, and Perfectly Inelastic Collisions

6:39 Position of the Center of Mass of a System of Particles

7:19 Velocity of the Center of Mass of a System of Particles

7:54 Acceleration of the Center of Mass of a System of Particles

8:31 Center of Mass of a Rigid Object with Shape

10:09 Volumetric, Surface, and Linear Mass Density

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Calculus based review of definite integrals, indefinite integrals, and derivatives as used in kinematics. Graphs of position, velocity, and acceleration as a function of time are compared using derivatives and integrals. Two of the uniformly accelerated motion (or kinematics) equations are derived using indefinite integrals.

For the calculus based AP Physics C mechanics exam.

Want Lecture Notes?

Content Times:

0:11 Rearranging the acceleration equation to get change in velocity

1:41 Rearranging the velocity equation to get change in position

2:06 Comparing graphs of position, velocity, and acceleration as a function of time

3:28 Using the integral to solve for one of the uniformly accelerated motion equations

4:44 Using the integral to solve for a second uniformly accelerated motion equation

FYI: I do not teach integrals until we get to Work. By then the students who are taking calculus concurrently with AP Physics C Mechanics have had enough experience with derivatives that they only freak out a little bit when I teach them integrals.

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