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19 October, 11:08

A rotating wheel has a constant angular acceleration. It has an angular velocity of 5.0 rad/s at time t = 0 s, and 3.0 s later has an angular velocity of 9.0 rad/s. What is the angular displacement of the wheel during the 3.0-s interval?

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  1. 19 October, 11:13
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    Angular displacement during 3 seconds is 21 rad

    Explanation:

    We have equation of motion v = u + at

    Initial velocity, u = 5 rad/s

    Final velocity, v = 9 rad/s

    Time, t = 3 s

    Substituting

    v = u + at

    9 = 5 + a x 3

    a = 1.33 rad/s²

    Angular acceleration is 1.33 rad/s²

    Now we have equation of motion v² = u² + 2as

    Initial velocity, u = 5 rad/s

    Final velocity, v = 9 rad/s

    Angular acceleration = 1.33 rad/s²

    Substituting

    v² = u² + 2as

    9² = 5² + 2 x 1.33 x s

    s = 21 radians

    Angular displacement during 3 seconds is 21 rad
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