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    Rotational or Angular Simple Harmonic Motion

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    Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material.

    1) By what factor would the frequency change?

    2) Would the frequency increase or decrease by the factor found in part (a)?
    increase or decrease?

    3) By what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency?

    4) Would the torsion constant need to be increased or decreased by the factor found in part (c)?
    increased or decreased?

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    https://brainmass.com/physics/circular-motion/rotationsal-angular-simple-harmonic-motion-74045

    Solution Preview

    Please see the attachment.

    Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material.

    Answer:

    This is the case of the rotational simple harmonic motion, and the frequency f of the oscillation is given by

    where K is the torque constant ( ...

    Solution Summary

    The balance of a clock have a wheel and making angular simple harmonic motion. The frequency is calculated when the dimensions of the wheel are changed.

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