# Angular Frequency(OCR A Level Physics)

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Katie M

Expertise

Physics

## Angular Frequency

• Angular frequency, ⍵, in oscillations is equivalent to angular velocity in circular motion
• It can is defined as:

The rate of change of angular displacement with respect to time

• This can be written as an equation:

• Where:
• ⍵ = angular frequency (rad s-1)
• 2π = circumference of a circle
• T = time period (s)
• f = frequency of oscillation (Hz)

#### Worked example

A cuckoo in a cuckoo clock emerges from a fully compressed position to a fully extended position in 1.5 seconds.

Calculate the angular frequency of the cuckoo as it emerges from the clock.

Step 1: Consider the motion of the cuckoo

• The cuckoo goes from being fully compressed to fully extended which means that it travels for an angular displacement of half a circle and not a full circle
• So, instead of 2π the distance will be π

Step 2: Substitute into the equation for angular velocity and time period

ω = = 2.09 rad s-1

Step 3: State the final answer

• The angular frequency of the cuckoo as it emerges from the clock is 2.1 rad s-1 (2 s.f.)

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