# A-level Physics/Equation Sheet

Equations, constants, and other useful data that the A-level student of physics is required to memorise.

## Forces and Motion

### Newtonian Mechanics

#### Conventions

• $\vec{v}_0\$ denotes initial velocity
• $\vec{v}\$ denotes final velocity
• $\vec{a}\$ denotes acceleration
• $\vec{s}$ denotes displacement
• $t\$ denotes time
• $W\$ denotes work done
• $m,\ m_i$ denotes mass or mass of object $i$
• $P\$ denotes Power
• A vector without it's arrow implies the magnitude of the vector, e.g. $b=\left|\vec{b}\right|$

#### Kinematic Equations

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

#### Force and Momentum

• $\vec{p} = m \vec{v}$
• $\vec{F_{net}} = m \vec{a}$
• $\vec{F} = \frac{\Delta \vec{p}}{\Delta t} = \frac {m \Delta \vec{v}}{\Delta t} = \frac{d \vec{p}}{dt}$
• $\vec{F_g}=\frac{Gm_1m_2}{r^2}$

#### Work and Energy

• $E_g = mgh\$ For small heights where $g$ can be treated as constant
• $E_g = \frac{-Gm_1m_2}{r}$ (for any height)
• $E_K = \frac{1}{2}mv^2$
• $W = \vec{F} \cdot \Delta \vec{x} = \int \vec{F} \cdot d \vec{x}$
• $P = \frac {\Delta W}{\Delta t} = \frac{dW}{dt}$