First slide

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

A

$(M + \frac{m}{4}) R^{2}$
B

$(M + m) R^{2}$
C

$(M + 3 m) R^{2}$
D

$(\frac{M + 3 m}{2}) R^{2}$

Solution

Moment of inertia of the ring is ${MR}^{2}$ and that of each spoke is $\frac{{mR}^{2}}{3}$ .
Total moment of inertia ${MR}^{2} + \frac{{mR}^{2}}{3} \times 3 = (M + m) R^{2}$

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