Angular velocity (\omega)
Circular Motion - OCR A-Level Physics
Key Definition
Angular velocity ($\omega$)
The rate of change of angular displacement, measured in radians per second ($\text{rad s}^{-1}$).
The rate of change of angular displacement, measured in radians per second ($\text{rad s}^{-1}$).
Key Definition
Radian
The angle subtended at the centre of a circle by an arc equal in length to the radius. One full revolution = $2\pi$radians.
The angle subtended at the centre of a circle by an arc equal in length to the radius. One full revolution = $2\pi$radians.
$$\begin{aligned}
\omega &= \frac{2\pi}{T} \\
&= 2\pi f
\end{aligned}$$
- For uniform circular motionMotion in a circle at constant speed. The velocity is always changing direction, so acceleration is centripetal., the speed is constant but the velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. is continuously changing direction.
- One complete revolution corresponds to an angular displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). of $2\pi$radians ($360^\circ$).
- All points on a rotating rigid body have the same angular velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.The rate of change of angular displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).. The angle swept per unit time for an object moving in a circle. Measured in rad s⁻¹. but different linear speeds depending on their distance from the axis.
- Angular velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.The rate of change of angular displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).. The angle swept per unit time for an object moving in a circle. Measured in rad s⁻¹. is sometimes called angular frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz)., especially in the context of SHM.
Common Mistake
MEDIUM
Wrong: Confusing angular velocityThe rate of change of angular displacement. The angle swept per unit time for an object moving in a circle. Measured in rad s⁻¹. ($\text{rad s}^{-1}$) with frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). (Hz) or forgetting the $2\pi$ factor.
Right: $\omega = 2\pi f$. Angular velocity is always $2\pi$ times the frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).. If $T = 0.5 \text{ s}$, then $f = 2 \text{ Hz}$ but $\omega = 4\pi \text{ rad s}^{-1}$.
Right: $\omega = 2\pi f$. Angular velocity is always $2\pi$ times the frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).. If $T = 0.5 \text{ s}$, then $f = 2 \text{ Hz}$ but $\omega = 4\pi \text{ rad s}^{-1}$.