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
- $\frac{d}{dx}\sin x=\cos x$
- $\frac{d}{dx}\cos x=-\sin x$
- $\frac{d}{dx}\tan x=\sec^2 x$
- $\int \sin x dx=-\cos x+C$
- $\int \cos x dx=\sin x+C$
- $\int \tan x dx=\ln |\sec x|+C$
