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AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Exam: 1 hour 30 minutes - 35 MCQ (70 min, 50%) + 3 FRQ (45 min, 50%) Calculator: Allowed (graphing calculator required) Note: Calculus-based; distinct from AP Physics 1 (algebra-based)

Section	Format	Questions	Time	Weight
Section I	Multiple Choice (MCQ)	35	70 min	50%
Section II	Free Response (FRQ)	3	45 min	50%

Science Practices (Skills Tested)

Skill	Name	Exam Weight
1	Visual Representations	12%-18%
2	Question and Methods	8%-12%
3	Representing Data and Phenomena	12%-18%
4	Data Analysis	12%-18%
5	Theoretical Arguments	8%-12%
6	Mathematical Routines	18%-24%
7	Connection Across Topics	12%-18%

FRQ Types

Type	Description
Quantitative/Qualitative Translation	Translate between representations
Paragraph Argument	Long-form written justification
Lab Design	Experimental procedure and analysis

FRQ Tips

Energy + Rotation combination: Mechanics FRQs frequently combine rotational dynamics with energy or momentum - always check if you need $K_{rot} = \frac{1}{2}I\omega^2$ in addition to translational terms
Calculus-based work: For non-constant forces, set up integral correctly (e.g., $W = \int \vec{F} \cdot d\vec{r}$ , $U = -\int F \\,dx$ )
Conservation vs. W-nc: State clearly whether you're using conservation of energy or work-energy theorem; include $W_{nc}$ when friction/air resistance is present
Angular momentum problems: Use $L = I\omega$ for fixed-axis rotation; verify axis is indeed fixed before applying
Momentum in collisions: For perfectly inelastic collisions, remember $v_f = \frac{m_1v_1 + m_2v_2}{m_1+m_2}$
Free-body diagrams: Draw one per distinct object; label all forces with correct physics names (weight = mg, not just "gravity")
Partials are real: Set up correct equations even if you can't solve them - partial credit is substantial

Unit 1: Kinematics

Displacement

\Delta \vec{r} = \vec{r}_f - \vec{r}_i

Practice

Instantaneous Vs. Average Velocity/acceleration

\vec{v}(t) = \lim_{\Delta t \to 0} \frac{\Delta \vec{r}}{\Delta t} = \frac{d\vec{r}}{dt}

Practice

More Concepts About Unit 1

Unit 2: Force and Translational Dynamics

System Boundary

Define what objects are included in the system. Internal forces : Forces between objects within the system External forces : Forces from objects outside the system ...

Practice

Center Of Mass For Discrete And Continuous Systems

\vec{r}_{cm} = \frac{\sum_{i=1}^{N} m_i \vec{r}_i}{\sum_{i=1}^{N} m_i}

Practice

More Concepts About Unit 2

Unit 3: Work, Energy, and Power

$K = \frac{1}{2}m v^2$

K = \frac{1}{2}mv^2

Practice

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

W = \vec{F} \cdot \vec{d} = Fd\cos\theta

Practice

More Concepts About Unit 3

Unit 4: Linear Momentum

Defining Linear Momentum

\vec{p} = m\vec{v}

Practice

Defining Impulse

\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i

Practice

More Concepts About Unit 4

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

360 degrees = 2\pi

Practice

Angular Velocity (ω）

\omega = \frac{d\theta}{dt}

Practice

More Concepts About Unit 5

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

\vec{L} = \vec{r} \times \vec{p} = \vec{r} \times m\vec{v}

Practice

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Vector cross product form. L = Iω (rigid body about fixed axis) : Simplified angular momentum. ...

Practice

More Concepts About Unit 6

Unit 7: Oscillations

Definition: $a = -\omega^2 x$

a = -\omega^2 x

Practice

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$

\frac{d^2x}{dt^2} = -\omega^2 x

Practice

More Concepts About Unit 7

Select Subject

Select Unit

AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Exam: 1 hour 30 minutes - 35 MCQ (70 min, 50%) + 3 FRQ (45 min, 50%) Calculator: Allowed (graphing calculator required) Note: Calculus-based; distinct from AP Physics 1 (algebra-based)

Section	Format	Questions	Time	Weight
Section I	Multiple Choice (MCQ)	35	70 min	50%
Section II	Free Response (FRQ)	3	45 min	50%

Science Practices (Skills Tested)

Skill	Name	Exam Weight
1	Visual Representations	12%-18%
2	Question and Methods	8%-12%
3	Representing Data and Phenomena	12%-18%
4	Data Analysis	12%-18%
5	Theoretical Arguments	8%-12%
6	Mathematical Routines	18%-24%
7	Connection Across Topics	12%-18%

FRQ Types

Type	Description
Quantitative/Qualitative Translation	Translate between representations
Paragraph Argument	Long-form written justification
Lab Design	Experimental procedure and analysis

FRQ Tips

Energy + Rotation combination: Mechanics FRQs frequently combine rotational dynamics with energy or momentum - always check if you need $K_{rot} = \frac{1}{2}I\omega^2$ in addition to translational terms
Calculus-based work: For non-constant forces, set up integral correctly (e.g., $W = \int \vec{F} \cdot d\vec{r}$ , $U = -\int F \\,dx$ )
Conservation vs. W-nc: State clearly whether you're using conservation of energy or work-energy theorem; include $W_{nc}$ when friction/air resistance is present
Angular momentum problems: Use $L = I\omega$ for fixed-axis rotation; verify axis is indeed fixed before applying
Momentum in collisions: For perfectly inelastic collisions, remember $v_f = \frac{m_1v_1 + m_2v_2}{m_1+m_2}$
Free-body diagrams: Draw one per distinct object; label all forces with correct physics names (weight = mg, not just "gravity")
Partials are real: Set up correct equations even if you can't solve them - partial credit is substantial

Unit 1: Kinematics

Displacement

\Delta \vec{r} = \vec{r}_f - \vec{r}_i

Practice

Instantaneous Vs. Average Velocity/acceleration

\vec{v}(t) = \lim_{\Delta t \to 0} \frac{\Delta \vec{r}}{\Delta t} = \frac{d\vec{r}}{dt}

Practice

More Concepts About Unit 1

Unit 2: Force and Translational Dynamics

System Boundary

Define what objects are included in the system. Internal forces : Forces between objects within the system External forces : Forces from objects outside the system ...

Practice

Center Of Mass For Discrete And Continuous Systems

\vec{r}_{cm} = \frac{\sum_{i=1}^{N} m_i \vec{r}_i}{\sum_{i=1}^{N} m_i}

Practice

More Concepts About Unit 2

Unit 3: Work, Energy, and Power

$K = \frac{1}{2}m v^2$

K = \frac{1}{2}mv^2

Practice

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

W = \vec{F} \cdot \vec{d} = Fd\cos\theta

Practice

More Concepts About Unit 3

Unit 4: Linear Momentum

Defining Linear Momentum

\vec{p} = m\vec{v}

Practice

Defining Impulse

\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i

Practice

More Concepts About Unit 4

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

360 degrees = 2\pi

Practice

Angular Velocity (ω）

\omega = \frac{d\theta}{dt}

Practice

More Concepts About Unit 5

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

\vec{L} = \vec{r} \times \vec{p} = \vec{r} \times m\vec{v}

Practice

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Vector cross product form. L = Iω (rigid body about fixed axis) : Simplified angular momentum. ...

Practice

More Concepts About Unit 6

Unit 7: Oscillations

Definition: $a = -\omega^2 x$

a = -\omega^2 x

Practice

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$

\frac{d^2x}{dt^2} = -\omega^2 x

Practice

More Concepts About Unit 7

Select Subject

Select Unit

AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Exam: 1 hour 30 minutes - 35 MCQ (70 min, 50%) + 3 FRQ (45 min, 50%) Calculator: Allowed (graphing calculator required) Note: Calculus-based; distinct from AP Physics 1 (algebra-based)

Section	Format	Questions	Time	Weight
Section I	Multiple Choice (MCQ)	35	70 min	50%
Section II	Free Response (FRQ)	3	45 min	50%

Science Practices (Skills Tested)

Skill	Name	Exam Weight
1	Visual Representations	12%-18%
2	Question and Methods	8%-12%
3	Representing Data and Phenomena	12%-18%
4	Data Analysis	12%-18%
5	Theoretical Arguments	8%-12%
6	Mathematical Routines	18%-24%
7	Connection Across Topics	12%-18%

FRQ Types

Type	Description
Quantitative/Qualitative Translation	Translate between representations
Paragraph Argument	Long-form written justification
Lab Design	Experimental procedure and analysis

FRQ Tips

Energy + Rotation combination: Mechanics FRQs frequently combine rotational dynamics with energy or momentum - always check if you need $K_{rot} = \frac{1}{2}I\omega^2$ in addition to translational terms
Calculus-based work: For non-constant forces, set up integral correctly (e.g., $W = \int \vec{F} \cdot d\vec{r}$ , $U = -\int F \\,dx$ )
Conservation vs. W-nc: State clearly whether you're using conservation of energy or work-energy theorem; include $W_{nc}$ when friction/air resistance is present
Angular momentum problems: Use $L = I\omega$ for fixed-axis rotation; verify axis is indeed fixed before applying
Momentum in collisions: For perfectly inelastic collisions, remember $v_f = \frac{m_1v_1 + m_2v_2}{m_1+m_2}$
Free-body diagrams: Draw one per distinct object; label all forces with correct physics names (weight = mg, not just "gravity")
Partials are real: Set up correct equations even if you can't solve them - partial credit is substantial

Unit 1: Kinematics

Displacement

\Delta \vec{r} = \vec{r}_f - \vec{r}_i

Practice

Instantaneous Vs. Average Velocity/acceleration

\vec{v}(t) = \lim_{\Delta t \to 0} \frac{\Delta \vec{r}}{\Delta t} = \frac{d\vec{r}}{dt}

Practice

More Concepts About Unit 1

Unit 2: Force and Translational Dynamics

System Boundary

Define what objects are included in the system. Internal forces : Forces between objects within the system External forces : Forces from objects outside the system ...

Practice

Center Of Mass For Discrete And Continuous Systems

\vec{r}_{cm} = \frac{\sum_{i=1}^{N} m_i \vec{r}_i}{\sum_{i=1}^{N} m_i}

Practice

More Concepts About Unit 2

Unit 3: Work, Energy, and Power

$K = \frac{1}{2}m v^2$

K = \frac{1}{2}mv^2

Practice

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

W = \vec{F} \cdot \vec{d} = Fd\cos\theta

Practice

More Concepts About Unit 3

Unit 4: Linear Momentum

Defining Linear Momentum

\vec{p} = m\vec{v}

Practice

Defining Impulse

\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i

Practice

More Concepts About Unit 4

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

360 degrees = 2\pi

Practice

Angular Velocity (ω）

\omega = \frac{d\theta}{dt}

Practice

More Concepts About Unit 5

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

\vec{L} = \vec{r} \times \vec{p} = \vec{r} \times m\vec{v}

Practice

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Vector cross product form. L = Iω (rigid body about fixed axis) : Simplified angular momentum. ...

Practice

More Concepts About Unit 6

Unit 7: Oscillations

Definition: $a = -\omega^2 x$

a = -\omega^2 x

Practice

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$

\frac{d^2x}{dt^2} = -\omega^2 x

Practice

More Concepts About Unit 7

AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Science Practices (Skills Tested)

FRQ Types

FRQ Tips

Unit 1: Kinematics

Displacement

Instantaneous Vs. Average Velocity/acceleration

Unit 2: Force and Translational Dynamics

System Boundary

Center Of Mass For Discrete And Continuous Systems

Unit 3: Work, Energy, and Power

K=12mv2K = \frac{1}{2}m v^2K=21​mv2

W=F⋅d=Fdcos⁡θW = \mathbf{F} \cdot \mathbf{d} = Fd \cos\thetaW=F⋅d=Fdcosθ

Unit 4: Linear Momentum

Defining Linear Momentum

Defining Impulse

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

Angular Velocity (ω）

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

L=r×pL = \mathbf{r} \times \mathbf{p}L=r×p (Particle)

Unit 7: Oscillations

Definition: a=−ω2xa = -\omega^2 xa=−ω2x

Differential Equation: d2xdt2=−ω2x\frac{d^2x}{dt^2} = -\omega^2 xdt2d2x​=−ω2x

AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Science Practices (Skills Tested)

FRQ Types

FRQ Tips

Unit 1: Kinematics

Displacement

Instantaneous Vs. Average Velocity/acceleration

Unit 2: Force and Translational Dynamics

System Boundary

Center Of Mass For Discrete And Continuous Systems

Unit 3: Work, Energy, and Power

K=12mv2K = \frac{1}{2}m v^2K=21​mv2

W=F⋅d=Fdcos⁡θW = \mathbf{F} \cdot \mathbf{d} = Fd \cos\thetaW=F⋅d=Fdcosθ

Unit 4: Linear Momentum

Defining Linear Momentum

Defining Impulse

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

Angular Velocity (ω）

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

L=r×pL = \mathbf{r} \times \mathbf{p}L=r×p (Particle)

Unit 7: Oscillations

Definition: a=−ω2xa = -\omega^2 xa=−ω2x

Differential Equation: d2xdt2=−ω2x\frac{d^2x}{dt^2} = -\omega^2 xdt2d2x​=−ω2x

AP Physics C: Mech

Physics C: Mechanics

AP Physics C: Mechanics Complete Notes

Science Practices (Skills Tested)

FRQ Types

FRQ Tips

Unit 1: Kinematics

Displacement

Instantaneous Vs. Average Velocity/acceleration

Unit 2: Force and Translational Dynamics

System Boundary

Center Of Mass For Discrete And Continuous Systems

Unit 3: Work, Energy, and Power

K=12mv2K = \frac{1}{2}m v^2K=21​mv2

W=F⋅d=Fdcos⁡θW = \mathbf{F} \cdot \mathbf{d} = Fd \cos\thetaW=F⋅d=Fdcosθ

Unit 4: Linear Momentum

Defining Linear Momentum

Defining Impulse

Unit 5: Torque and Rotational Dynamics

Angular Displacement (θ)

Angular Velocity (ω）

Unit 6: Energy and Momentum of Rotating Systems

Definition Of Angular Momentum For A Particle

L=r×pL = \mathbf{r} \times \mathbf{p}L=r×p (Particle)

Unit 7: Oscillations

Definition: a=−ω2xa = -\omega^2 xa=−ω2x

$K = \frac{1}{2}m v^2$

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Definition: $a = -\omega^2 x$

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$

$K = \frac{1}{2}m v^2$

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Definition: $a = -\omega^2 x$

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$

$K = \frac{1}{2}m v^2$

$W = \mathbf{F} \cdot \mathbf{d} = Fd \cos\theta$

$L = \mathbf{r} \times \mathbf{p}$ (Particle)

Definition: $a = -\omega^2 x$

Differential Equation: $\frac{d^2x}{dt^2} = -\omega^2 x$