Key Equations
Circular Motion - OCR A-Level Physics
On Data Sheet
Not on Data Sheet
Angular velocity from period
$$\omega = \frac{2\pi}{T}$$
- Where:
- $\omega$ = rad \(s^{-1}\)
- $T$ = s
Use when given the period of rotation. Also on the data sheet.
Linear speed from angular velocity
$$v = r\omega$$
- Where:
- $v$ = m \(s^{-1}\)
- $r$ = m
- $\omega$ = rad \(s^{-1}\)
Links translational and rotational descriptions. Points further from the axis have greater v for the same \omega.
Centripetal acceleration (speed form)
$$a = \frac{v^2}{r}$$
- Where:
- $a$ = m \(s^{-2}\)
- $v$ = m \(s^{-1}\)
- $r$ = m
Use when given linear speed. Always directed towards the centre.
Centripetal acceleration (angular form)
$$a = r\omega^2$$
- Where:
- $a$ = m \(s^{-2}\)
- $r$ = m
- $\omega$ = rad \(s^{-1}\)
Use when given angular velocity. Equivalent to \(v^{2}\)/r via v = r\omega.
Centripetal force (speed form)
$$F = \frac{mv^2}{r}$$
- Where:
- $F$ = N
- $m$ = kg
- $v$ = m \(s^{-1}\)
- $r$ = m
The resultant force towards the centre required for circular motion. Not a new type of force.
Centripetal force (angular form)
$$F = mr\omega^2$$
- Where:
- $F$ = N
- $m$ = kg
- $r$ = m
- $\omega$ = rad \(s^{-1}\)
Alternative form using angular velocity.
Angular velocity from frequency
$$\omega = 2\pi f$$
- Where:
- $\omega$ = rad \(s^{-1}\)
- $f$ = Hz
Must memorise. Not explicitly on the data sheet in this form but follows directly from \omega = 2\pi/T and f = 1/T.