A LevelPhysicsOCRRevision Notes5. Newtonian World & AstrophysicsSimple Harmonic OscillationsAngular Frequency

Angular Frequency (OCR A Level Physics): Revision Note

Exam code: H556

Katie M

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Katie M

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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 space equals space fraction numerator 2 straight pi over denominator T end fraction space equals space 2 straight pi f

  • Where:

    • omega = angular frequency (rad s-1)

    • 2 straight pi = circumference of a circle

    • T = time period (s)

    • space 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 Acan 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 space cos space theta

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

5-5-2-angular-frequency-oscillation_ocr-al-physics

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

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. 

Answer:

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

5-5-2-angular-frequency-we_ocr-al-physics

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

 omega space equals space fraction numerator 2 straight pi over denominator T end fraction= fraction numerator straight pi over denominator 1.5 end fraction = 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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Katie M

Author: Katie M

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Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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