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6 September, 07:27

Consider a rigid body that rotates but whose center of mass is at rest. a. Trueb. false: the rotational kinetic energy of the entire object is equivalent to the sum of the translational kinetic energy of each small piece of the object.

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  1. 6 September, 08:19
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    True

    It is correct as the total rotational energy is the sum of transnational kinetic energy of each small piece of the object.

    Consider a rigid body made of small particles each of mass dm have same angular velocity ω and the radius of the rotational path is r.

    The velocity of each particle is v = r ω

    So, the kinetic energy of each particle is

    dK = 0.5 dm x v² = 0.5 x dm x r² x ω²

    The total kinetic energy

    K = 0.5 x I ω²

    where, I is the moment of inertia
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