Key Equations
Circular Motion — AQA A-Level Physics
On Data Sheet
Not on Data Sheet
Angular speed
$$\begin{aligned}
\omega &= \frac{\Delta \theta}{\Delta t} \\
&= \frac{v}{r} \\
&= 2\pi f \\
&= \frac{2\pi}{T}
\end{aligned}$$
- Where:
- $\omega$ = angular speed (rad \(s^{-1}\))
- $v$ = linear speed (m \(s^{-1}\))
- $r$ = radius (m)
- $f$ = frequency (Hz)
- $T$ = time period (s)
All four forms are equivalent. Choose based on given data.
Angular displacement
$$\Delta \theta = \frac{\Delta s}{r}$$
- Where:
- $\Delta \theta$ = angular displacement (rad)
- $\Delta s$ = arc length (m)
- $r$ = radius (m)
Both arc length and radius must be in the same units.
Centripetal acceleration
$$\begin{aligned}
a &= \frac{\(v^{2}\)}{r} \\
&= r\omega^2 \\
&= v\omega
\end{aligned}$$
- Where:
- $a$ = centripetal acceleration (m \(s^{-2}\))
- $v$ = linear speed (m \(s^{-1}\))
- $r$ = radius (m)
- $\omega$ = angular speed (rad \(s^{-1}\))
All three forms on the data sheet. a = v omega is often overlooked but useful.
Centripetal force
$$\begin{aligned}
F &= \frac{mv^2}{r} \\
&= mr\omega^2 \\
&= mv\omega
\end{aligned}$$
- Where:
- $F$ = centripetal force (N)
- $m$ = mass (kg)
- $v$ = linear speed (m \(s^{-1}\))
- $r$ = radius (m)
- $\omega$ = angular speed (rad \(s^{-1}\))
From Newton's second law: F = ma applied to each acceleration form.