A solid uniform sphere of mass M=0.540 kg has a radius R=0.200m and rotates arou

Question

A solid uniform sphere of mass M=0.540 kg has a radius R=0.200m and rotates around a fixed axis with angular velocity =48.0rad/s.
(a) What is the kinetic energy if the axis of rotation passesthrough the center of the sphere ?

(b) What is the kinetic energy if the axis of rotation is tangentto the surface of the sphere ? A solid uniform sphere of mass M=0.540 kg has a radius R=0.200m and rotates around a fixed axis with angular velocity =48.0rad/s.
(a) What is the kinetic energy if the axis of rotation passesthrough the center of the sphere ?

(b) What is the kinetic energy if the axis of rotation is tangentto the surface of the sphere ?

Explanation / Answer

mass m = 0.54 kg radius r = 0.2 m angular velocity w = 48 rad / s (a). Moment of inertia of the sphere I = ( 2/ 5 ) m r ^2                                                         = 0.00864 kg m ^ 2 the kinetic energy if the axis of rotation passes through thecenter of the sphere = ( 1/ 2) I w ^ 2                                                                                                                       = 9.9553 J (b).Moment of inertia along the axis of rotation is tangent tothe surface of the sphere  I ' = ( 7 / 5 ) m r ^ 2                                                                                                                                    = 0.03024 kg m ^ 2 So, the kinetic energy if the axis of rotation is tangent tothe surface of the sphere = ( 1/ 2) I ' w ^ 2                                                                                                                          = 34.836 J

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