Moment of intertia

Question

A wheel comprises of a ring of radius R and M and three spokes of mass m each moment of inertia of the wheel about its axis is:

Easy

Solution

Moment of inertia of the ring is ${\mathrm{MR}}^{2}$ and that of each spoke is $\frac{{\mathrm{mR}}^{2}}{3}$ .

Total moment of inertia ${\mathrm{MR}}^{2}+\frac{{\mathrm{mR}}^{2}}{3}\times 3=\left(\mathrm{M}+\mathrm{m}\right){\mathrm{R}}^{2}$

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