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24 September, 20:23

A sphere of uniform density, with mass 18 kg and radius 0.8 m, is located at the origin and rotates around an axis parallel with the axis. If you stand somewhere on the axis and look toward the origin at the sphere, the sphere spins counterclockwise. One complete revolution takes 0.7 s. What is the rotational angular momentum of the sphere? What is the rotational kinetic energy of the sphere? (Express your answer for rotational angular momentum in vector form.)

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  1. 24 September, 20:51
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    Given that,

    Mass of sphere M = 18kg

    Radius R = 0.8m

    Angular revolution is

    It completes 1 revolution in 0.7sec

    θ = 1 rev, t = 0.1sec

    1 rev = 2πrad

    Then, ω = θ / t

    ω = 2π/0.7 = 8.98 rad/s

    A. Angular momentum is given as

    L = Iω

    I is moment of inertial

    Moment of inertial of a sphere is given as

    I = 2/5 • MR²

    I = 2/5 * 18 * 0.8²

    I = 4.61 kgm²

    Then,

    L = Iω

    L = 4.61 * 8.98

    L = 41.38 kgm²/s

    Rotational kinetic energy

    K. E = ½Iω²

    K. E = ½ * 4.61 * 8.98²

    K. E = 185.88 J
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