The 800-mg balance wheel of a certain clock is made up of a thin metal ring of radius \(15 \mathrm{~mm}\) connected by spokes of negligible mass to a fine suspension fiber as in Figure 15. 31. The back-and-forth twisting of the fiber causes the wheel to move in simple harmonic motion with period \(T\). The clock ticks four times each second, with the interval between ticks equal to \(T / 2\).

(a) Determine the rotational inertia \(I\) of the balance wheel.

(b) What is the torsional constant of the fiber that drives the balance wheel?

Data from Figure 15.31

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support fiber max 0 +9