A-level Physics/Equation Sheet

Equations, constants and other useful data that you will be required to memorize.

Forces and motion

See also Symbols for Physical Quantities.

Newtonian Mechanics

Kinematic Equations

• $\overrightarrow{v}=\frac{\mathrm{\Delta }\overrightarrow{s}}{\mathrm{\Delta }t}=\frac{d\overrightarrow{s}}{dt}$
• $\overrightarrow{a}=\frac{\mathrm{\Delta }\overrightarrow{v}}{\mathrm{\Delta }t}=\frac{d\overrightarrow{v}}{dt}$
• $\mathrm{\Delta }v=v_0+a\mathrm{\Delta }t$
• $v^2=v_0^2+2a\mathrm{\Delta }s$
• $s=s_0+v_0\mathrm{\Delta }t+\frac{1}{2}a(\mathrm{\Delta }t{)}^2$
• $\mathrm{\Delta }s=\frac{v_0+v}{2}\cdot \mathrm{\Delta }t$

Force and Momentum

• $\overrightarrow{p}=m\overrightarrow{v}$
• $\overrightarrow{F_{net}}=m\overrightarrow{a}$
• $\overrightarrow{F}=\frac{\mathrm{\Delta }\overrightarrow{p}}{\mathrm{\Delta }t}=\frac{m\mathrm{\Delta }\overrightarrow{v}}{\mathrm{\Delta }t}=\frac{d\overrightarrow{p}}{dt}$
• $\overrightarrow{F_g}=\frac{GmM}{r^2}\hat{r}$

Work and Energy

• $E_g=mgh$ (for small heights only)
• $E_g=\frac{-GmM}{r}$ (for any height)
• $E_K=\frac{1}{2}m{v}^2$
• $W=\overrightarrow{F}\cdot \mathrm{\Delta }\overrightarrow{x}=\int \overrightarrow{F}\cdot d\overrightarrow{x}$
• $P=\frac{\mathrm{\Delta }W}{\mathrm{\Delta }t}=\frac{dW}{dt}$

Where:

• $v_0$ = initial velocity
• v = final velocity
• a = acceleration
• s = displacement
• t = time
• W = work done
• m = mass
• M = different mass, for equations with 2 masses interacting