If an object is rolling without slipping, how does its linear speed compare to its rotational speed?

Question

If an object is rolling without slipping, how does its linear speed compare to its rotational speed?

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Sigridomena 2 months 2021-07-31T12:19:19+00:00 1 Answers 4 views 0

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    2021-07-31T12:20:51+00:00

    Answer:

    v = rw

    Explanation:

    When an object is rolling continuously without slipping, then every angle it rotates through, is equal to a distance the perimeter has rotated.

    If the object completes 10 revolutions and takes a particular time, let’s say t to complete it. The angular distance would then be 20 π rad, while its angular velocity will be 20 π/t

    The circumference will somehow translate to the distance it covers, which is 20πr, this means that the speed is 20πr/t

    So, like the question asked, the linear speed compared to angular speed is

    v : w

    20πr/t : 20πt, which can be simplified to

    r : 1

    In essence, v = rw

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