AP® Physics C: Mechanics Cheat Sheet

Prepare for AP Physics C: Mechanics with this detailed cheat sheet, covering kinematics, Newton’s laws, energy, momentum, rotation, oscillations, and gravitation. Ideal for quick review before exams or during problem-solving.

Download AP Physics C: Mechanics Cheat Sheet – Pdf

Unit 1: Kinematics

• Kinematics in One Dimension:
  • Displacement: \(\Delta x = x_f – x_i\)
  • Velocity: \(v = \frac{dx}{dt}\)
  • Acceleration: \(a = \frac{dv}{dt}\)
  • Equations of Motion:
    • \(v = v_0 + at\)
    • \(x = x_0 + v_0t + \frac{1}{2}at^2\)
    • \(v^2 = v_0^2 + 2a(x – x_0)\)
• Kinematics in Two Dimensions:
  • Position Vector: \(\vec{r} = x\hat{i} + y\hat{j}\)
  • Velocity Vector: \(\vec{v} = \frac{d\vec{r}}{dt} = v_x\hat{i} + v_y\hat{j}\)
  • Projectile Motion:
    • \(x(t) = v_{0x} t\)
    • \(y(t) = v_{0y} t – \frac{1}{2} g t^2\)
  • Relative Velocity: \(\vec{v}_{AB} = \vec{v}_A – \vec{v}_B\)

Unit 2: Newton’s Laws of Motion

• Newton’s First and Second Law:
  • First Law (Inertia): \(\vec{F}_{\text{net}} = 0 \Rightarrow \text{constant velocity}\)
  • Second Law: \(\vec{F}_{\text{net}} = m\vec{a}\)
  • Weight: W = mg
• Circular Motion:
  • Centripetal Acceleration: \(a_c = \frac{v^2}{r}\)​
  • Centripetal Force: \(F_c = m \frac{v^2}{r}\)
  • Uniform Circular Motion: Constant speed, changing velocity direction.
• Newton’s Third Law:
  • Action-Reaction: For every action, there is an equal and opposite reaction, \(\vec{F}_{AB} = -\vec{F}_{BA}\)​.

Unit 3: Work, Energy, and Power

• Work-Energy Theorem:
  • \(W = \Delta K = \frac{1}{2}mv_f^2 – \frac{1}{2}mv_i^2\)
• Forces and Potential Energy:
  • Gravitational Potential Energy: \(U_g = mgh\)
  • Elastic Potential Energy: \(U_s = \frac{1}{2} kx^2\)
  • Conservative Forces: \(\vec{F} = -\frac{dU}{dx}\)
• Conservation of Energy:
  • Mechanical Energy: E = K + U
  • Conservation: \(E_i = E_f\)​ (No non-conservative forces)
• Power:
  • Power: \(P = \frac{dW}{dt} = Fv\)
  • Units: Watts (W)

Unit 4: Systems of Particles and Linear Momentum

• Center of Mass:
  • Center of Mass (Discrete Particles): \(\vec{r}_{\text{cm}} = \frac{1}{M} \sum m_i \vec{r}_i\)
• Impulse and Momentum:
  • Momentum: \(\vec{p} = m\vec{v}\)
  • Impulse: \(\vec{J} = \Delta \vec{p} = \int \vec{F} dt\)
  • Impulse-Momentum Theorem: \(\vec{J} = \Delta \vec{p}\)
• Conservation of Linear Momentum:
  • Elastic Collisions: \(\vec{p}_{\text{initial}} = \vec{p}_{\text{final}}​, K_{\text{initial}} = K_{\text{final}}\)
  • Inelastic Collisions: \(\vec{p}_{\text{initial}} = \vec{p}_{\text{final}}\)​, \(K_{\text{initial}} > K_{\text{final}}\)

Unit 5: Rotation

• Torque and Rotational Statics:
  • Torque: \(\tau = rF \sin \theta\)
  • Rotational Equilibrium: \(\sum \tau = 0\)
• Rotational Kinematics:
  • Angular Displacement: \(\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2\)
  • Angular Velocity: \(\omega = \omega_0 + \alpha t\)
  • Angular Acceleration: \(\alpha = \frac{d\omega}{dt}\)
• Rotational Dynamics and Energy:
  • Rotational Inertia: \(I = \sum m_i r_i^2\)
  • Newton’s Second Law for Rotation: \(\tau = I\alpha\)
  • Rotational Kinetic Energy: \(K = \frac{1}{2} I \omega^2\)
• Angular Momentum and Its Conservation:
  • Angular Momentum: \(L = I \omega\)
  • Conservation of Angular Momentum: \(\vec{L}_{\text{initial}} = \vec{L}_{\text{final}}\)

Unit 6: Oscillations

• Simple Harmonic Motion (SHM):
  • Position: \(x(t) = A \cos(\omega t + \phi)\)
  • Velocity: \(v(t) = -A \omega \sin(\omega t + \phi)\)
  • Acceleration: \(a(t) = -A \omega^2 \cos(\omega t + \phi)\)
• Springs:
  • Hooke’s Law: \(F_s = -kx\)
  • Spring Constant: k, \(\omega = \sqrt{\frac{k}{m}}\)
• Pendulums:
  • Simple Pendulum: \(T = 2\pi \sqrt{\frac{L}{g}}\)
  • Angular Frequency: \(\omega = \sqrt{\frac{g}{L}}\)

Unit 7: Gravitation

• Gravitational Forces:
  • Newton’s Law of Universal Gravitation: \(F_g = G \frac{m_1 m_2}{r^2}\)
  • \(G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\)
• Gravitational Potential Energy:
  • \(U_g = -G \frac{m_1 m_2}{r}\)
• Orbits of Planets and Satellites:
  • Orbital Speed: \(v = \sqrt{\frac{GM}{r}}\)
  • Orbital Period: \(T = 2\pi \sqrt{\frac{r^3}{GM}}\)​​ (Kepler’s Third Law)

FRQ Tips

• Start with Free-Body Diagrams: Helps visualize forces and motion.
• Use Energy Methods: Especially for conservative systems.
• Check Units: Ensure consistency across all calculations.
• Apply Conservation Laws: Momentum, energy, and angular momentum are key.
• Explain All Steps: Clear reasoning can earn partial credit.