You are designing a flywheel to store large amounts of kinetic energy. Which one

Question

You are designing a flywheel to store large amounts of kinetic
energy. Which one of the following uniform shapes will be the
most effective for storing the greatest amount of kinetic
energy if all the objects have the same mass and same angular
velocity? PLEASE EXPLAIN!
A. A solid sphere of diameter D rotating about a diameter.
B. A solid cylinder of diameter D rotating about an axis perpendicular
to each face through its center.
C. A thin-walled hollow cylinder of diameter D rotating about
an axis perpendicular to the plane of the circular face at its
center.
D. A solid thin bar of length D rotating about an axis perpendicular
to it at its center.

Explanation / Answer

(c)

rotational kinetic energy = (1/2)I2

since they hae the same angular velocity, the energy is proportionate to the moments of inertia,I. Hence the option must have the largest moments of inertia

a (2/5)m(d/2)2 = 1/10 md2

b (1/2)m(d/2)2 =1/8 md2

c (1/2)m[(d/2)2 + (d/2)2] = 1/4 md2

d (1/12)md2 =1/12 md2

hence answer is (c)

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