AP Physics 2: The Ultimate Cheat Sheet

Unit 9 Thermodynamics

🔥 Heat & Gases

$PV = nRT = Nk_BT$

$K = \frac{3}{2}k_BT$

$\Delta U = Q + W$

$W = -P\Delta V$

Key Concept: Internal Energy ( $U$ ) is directly proportional to Temperature ( $T$ ). If temperature doesn’t change, $\Delta U = 0$ .

⚠️ Trap Alert The AP Physics formula sheet defines $W$ as work done ON the gas. If a gas expands ( $\Delta V$ is positive), it does work BY the gas, meaning the work ON the gas ( $W$ ) is negative! Also, always use Kelvin for Temperature!

Unit 10 Electric Force & Field

⚡ Electrostatics

$|F_E| = k\frac{|q_1 q_2|}{r^2}$

$\vec{E} = \frac{\vec{F_E}}{q}$

$\Delta V = \frac{\Delta U_E}{q}$

Key Concept: Electric Field ( $E$ ) is a vector (points away from positive). Electric Potential ( $V$ , voltage) is a scalar (just a number, like altitude).

⚠️ Trap Alert Never plug negative signs for charges into Coulomb’s Law ( $F_E$ ) or Electric Field ( $E$ ) formulas! Use the formula to find the magnitude, then use the “opposites attract” rule to figure out the direction.

Unit 11 DC Circuits

🔋 Current & Capacitors

$I = \frac{\Delta V}{R}$

$P = I\Delta V = I^2R$

$C = \frac{\kappa \epsilon_0 A}{d}$

Key Concept: In Series: Current ( $I$ ) is the same everywhere. In Parallel: Voltage ( $\Delta V$ ) is the same across all branches.

⚠️ Trap Alert In an RC circuit, an uncharged capacitor initially acts like a short circuit (a bare wire). After a long time, it becomes fully charged and acts like an open circuit (breaks the branch, no current flows through it).

Unit 12 Magnetism & Induction

🧲 Fields & Faraday’s Law

$F_M = qvB\sin\theta$

$\Phi_B = BA\cos\theta$

$\mathcal{E} = -N\frac{\Delta \Phi_B}{\Delta t}$

Key Concept: Magnetic forces only act on moving charges. A stationary charge in a magnetic field feels no force.

⚠️ Trap Alert The Right Hand Rule is for POSITIVE charges. If the problem asks about an electron, use your Left Hand (or use your Right Hand and flip the final answer 180 degrees!).

Unit 13 Geometric Optics

🌈 Mirrors & Lenses

$n_1\sin\theta_1 = n_2\sin\theta_2$

$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

$M = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$

Key Concept: A positive $d_i$ means the image is Real (can be projected on a screen). A negative $d_i$ means the image is Virtual.

⚠️ Trap Alert In reflection and refraction (Snell’s Law), ALWAYS measure your angles from the Normal (the perpendicular dashed line), never from the surface boundary itself!

Unit 14 Waves & Physical Optics

🌊 Interference

$v = f\lambda$

$d\sin\theta = m\lambda$

Key Concept: Wave speed ( $v$ ) is determined entirely by the medium. If a wave enters a new medium, speed and wavelength change, but Frequency ( $f$ ) remains constant.

⚠️ Trap Alert In Thin-Film Interference, if light reflects off a medium with a higher index of refraction, it undergoes a 180° ( $\lambda/2$ ) phase shift. You must count these “hard reflections” to know which formula to use!

Unit 15 Modern Physics

⚛️ Quantum & Nuclear

$E = hf$

$K_{max} = hf - \Phi$

$E = \Delta mc^2$

Key Concept: In nuclear decay equations, the total mass number (top) and total atomic number (bottom) must be equal on both sides of the arrow.

⚠️ Trap Alert In the Photoelectric Effect, increasing light Intensity (brightness) does NOT make ejected electrons move faster; it only ejects more of them. Only increasing the Frequency (color) increases their kinetic energy!