AP Physics C Mechanics Formula Sheet

The AP Physics C Mechanics exam is a challenging test that covers a wide range of topics. In order to do well on the exam, it is important to be familiar with the formulas that are tested. This formula sheet provides a comprehensive list of all of the formulas that are tested on the AP Physics C Mechanics exam.

Kinematics

• 1D Kinematics
  • $v=v_0+at$
  • $x=x_0+v_0t+\frac{1}{2}at^2$
  • $v^2=v_0^2+2a(x-x_0)$
  • $x_f=\frac{v_f+v_i}{2}t$
• 2D Kinematics
  • $v_x=v_{0x}+a_xt$
  • $x=x_0+v_{0x}t+\frac{1}{2}a_xt^2$
  • $v_y=v_{0y}+a_yt$
  • $y=y_0+v_{0y}t+\frac{1}{2}a_yt^2$
  • $v=\sqrt{v_x^2+v_y^2}$
  • $\theta=\tan^{-1}\left(\frac{v_y}{v_x}\right)$

Dynamics

• Newton’s Laws
  • $F=ma$
  • $F_n=mg$
  • $F_f=\mu F_n$
  • $v_f^2=v_i^2+2a(x_f-x_i)$
  • $W=F\cdot d$
  • $P=\frac{W}{t}$
• Circular Motion
  • $v=\frac{2\pi r}{T}$
  • $a=\frac{v^2}{r}$
  • $F_c=\frac{mv^2}{r}$
• Momentum
  • $p=mv$
  • $F=\frac{dp}{dt}$
  • $J=I\omega$
  • $K=\frac{1}{2}I\omega^2$
• Work and Energy
  • $W=\int F\cdot dx$
  • $K=\frac{1}{2}mv^2$
  • $U=-GMm/r$
  • $P=Fv$

Fluid Mechanics

• Fluid Properties
  • $\rho=\frac{m}{V}$
  • $P=\rho gh$
  • $\gamma=\rho g$
• Fluid Dynamics
  • $Q=Av$
  • $A_1v_1=A_2v_2$
  • $P_1+\frac{1}{2}\rho v_1^2+\rho gh_1=P_2+\frac{1}{2}\rho v_2^2+\rho gh_2$
  • $F_D=\frac{1}{2}\rho v^2C_DA$

Thermodynamics

• Temperature
  • $T_C=\frac{5}{9}(T_F-32)$
  • $T_K=T_C+273.15$
• Heat
  • $Q=mc\Delta T$
  • $Q=L\Delta m$
• Phase Transitions
  • $Q=mL$
• Ideal Gas Law
  • $PV=nRT$
• Thermodynamics
  • $\Delta U=Q-W$
  • $Q_{in}+Q_{out}+\sum W=0$
  • $S=k\ln W$

Waves

• Wave Properties
  • $v=\lambda f$
  • $f=\frac{1}{T}$
  • $y=A\sin(kx-\omega t)$
• Wave Mechanics
  • $v=\sqrt{\frac{T}{\mu}}$
  • $\lambda=\frac{v}{f}$
  • $I=\frac{P}{A}$
• Sound Waves
  • $v=\sqrt{\frac{\gamma RT}{M}}$
  • $I=\frac{P^2}{2\rho v}$
• Light Waves
  • $c=3\times10^8 \text{ m/s}$
  • $n=\frac{c}{v}$
  • $f=\frac{c}{\lambda}$

Other Formulas

• Constants
  • $g=9.8 \text{ m/s}^2$
  • $G=6.67\times10^{-11} \text{ m}^3\text{ kg}^{-1}\text{ s}^{-2}$
  • $R=8.31 \text{ J/mol K}$
  • $k=1.38\times10^{-23} \text{ J/K}$
  • $\epsilon_0=8.85\times10^{-12} \text{ F/m}$
  • $\mu_0=4\pi\times10^{-7} \text{ T m/A}$
• Trigonometry
  • $\sin^2\theta+\cos^2\theta=1$
  • $\tan\theta=\frac{\sin\theta}{\cos\theta}$
  • $\sin(2\theta)=2\sin\theta\cos\theta$
  • $\cos(2\theta)=\cos^2\theta-\sin^2\theta$
• Calculus
  • $\frac{d}{dx}\sin x=\cos x$
  • $\frac{d}{dx}\cos x=-\sin x$
  • $\frac{d}{dx}\tan x=\sec^2 x$
  • $\int \sin x dx=-\cos x+C$
  • $\int \cos x dx=\sin x+C$
  • $\int \tan x dx=\ln |\sec x|+C$