The rim of a steering wheel has a radius $R$ and a mass $M$ . There are five radial spokes that connect in the center, as shown in the figure. The spokes are thin rods of uniform mass density with length $R$ and mass $\frac{1}{4} M$ , and are evenly spaced around the wheel. Derive an expression for the moment of inertia $I$ of the steering wheel about an axis that passes perpendicularly through its center in terms of $M, R$ , and any necessary numerical and physical constants.

Question

The rim of a steering wheel has a radius

R

and a mass

M

. There are five radial spokes that connect in the center, as shown in the figure. The spokes are thin rods of uniform mass density with length

R

and mass

\frac{1}{4} M

, and are evenly spaced around the wheel. Derive an expression for the moment of inertia

I

of the steering wheel about an axis that passes perpendicularly through its center in terms of

M, R

, and any necessary numerical and physical constants.

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