Consider a rigid body that rotates but whose center of mass is at rest. True or false: the rotational kinetic energy of the entire object is

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Consider a rigid body that rotates but whose center of mass is at rest. True or 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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Gia Bảo 4 years 2021-08-15T23:48:57+00:00 1 Answers 55 views 0

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  1. Latifah
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    2021-08-15T23:50:29+00:00
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    Answer:

    True

    Explanation:

    Let us consider a rigid body which contains tiny particles of mass dm each. and the angular velocity ω for each of the particle is same and teh radius of rotation is r.

    the linear velocity, v = r ω

    The total kinetic energy is given by

    K=\int \frac{1}{2}dm v^{2}

    K=\int \frac{1}{2}dm r^{2}\omega^{2}

    K=\frac{1}{2}\times \omega^{2}\int dm r^{2}

    K = 1/2 Iω^2

    where I is the moment of inertia.

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