Question

The minute and hour hands of a clock have a common axis of rotation and equal masses. The minute hand is long, thin, and uniform; the hour hand is short, thick, and uniform. (a) Is the moment of inertia of the minute hand greater than, less than, or equal to the moment of inertia of the hour hand? (b) Choose the best explanation from among the following: A. The hands have equal masses, and hence equal moments of inertia. B. Having mass farther from the axis of rotation results in a greater moment of inertia. C. The more compact hour hand has its mass more concentrated and thus has the greater moment of inertia.

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(a) Solution: \textbf{Solution: }

Since the mass of the minute hand is equal to the mass of the hour hand.

As the textbook mentions that the moment of inertia of a disk is given by

I=12 m r2\begin{align*} I &= \dfrac{1}{2} ~ m ~ r^{2} \\ \end{align*}

Since the minute hand is long, thin, and uniform and the hour hand is short, thick, and uniform, then the moment of inertia of the minute hand would be greater than that of the hour hand. Because the center of mass of the minute hand lies farther away from the axis of rotation as compared to the hour hand.

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