A solid sphere of radius R, a solid cylinder of radius R, and a rod of length R

Question

A solid sphere of radius R, a solid cylinder of radius R, and a rod of length R all have the same mass, and all three are rotating with the same angular velocity The sphere is rotating around an axis through its center. The cylinder is rotating around its long axis, and the rod is rotating around an axis through its center but perpendicular to the rod Which one has the greatest rotational kinetic energy? the sphere the cylinder the rod the rod and the cylinder have the same rotational kinetic energy they all have the same kinetic energy

Explanation / Answer

here,

as the masses and angular speed of all three are same

moment of inertia of solid sphere, Is = 2/5 * m * r^2

moment of inertia of cyclinder , Ic = 0.5 * m * r^2

moment of inertia of rod , Ir = m * r^2 /12

rotational kinetic energy is directlt proportional to moment of inertia

therefore ,cyclinder has the greatest rotational kinetic energy

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