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27 June, 05:01

A solid cylinder of mass 12.0 kg and radius 0.250 m is free to rotate without friction around its central axis. If you do 75.0 J of work on the cylinder to increase its angular speed, what will be its final angular speed if the cylinder starts from rest?

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  1. 27 June, 05:13
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    20 rad/s

    Explanation:

    mass, m = 12 kg

    radius, r = 0.250 m

    Moment of inertia of cylinder, I = 1/2 mr²

    I = 0.5 x 12 x 0.250 x 0.250 = 0.375 kgm^2

    Work done = Change in kinetic energy

    Initial K = 0

    Final K = 1/2 Iω²

    W = 1/2 Iω²

    ω² = 2W / I = 2 x 75 / (0.375)

    ω = 20 rad/s

    Thus, the final angular velocity is 20 rad/s.
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