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Angular Frequency (OCR A Level Physics)

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Katie M

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Katie M

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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:

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

  • Where:

    • ⍵ = angular frequency (rad s-1)

    • 2π = circumference of a circle

    • T = time period (s)

    • f = frequency of oscillation (Hz)

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

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

ω = 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

    Expertise: Physics

    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.