Angular Frequency (OCR A Level Physics): Revision Note

Angular Frequency

• The angular frequency $\omega$ of an oscillation describes how quickly an oscillator cycles through its motion

• Angular frequency is defined as:

The rate of change of angular position with respect to time

• It can be written as an equation:

$\omega =\frac{2\mathrm{\pi }}{T}=2\mathrm{\pi }f$

• Where:

  • $\omega$ = angular frequency (rad s^-1)

  • $2\mathrm{\pi }$ = circumference of a circle

  • $T$ = time period (s)

  • $f$ = frequency of oscillation (Hz)

• The angular frequency of an object moving in simple harmonic motion is equivalent to the angular speed of an object undergoing uniform circular motion 

• For example, a mass-spring system oscillating with amplitude $A$can be represented by a particle moving in a circle with radius $A$

  • Along the x-axis, the displacement for both systems can be described by $A\cos \theta$

  • The time taken to complete one oscillation, or revolution, is equal to period $T$

The angular frequency of a mass-spring system is similar to a particle undergoing uniform circular motion