Question

A student stands on a freely rotating platform, as shown in Fig. 10 - 10 . With his arms extended, his rotational frequency is $0.25$ rev/s. But when he draws his arm in, that frequency becomes $0.80$ rev/s. Find the ratio of his moment of inertia in the first case to that in the second. Because there is no external torque on the system (why?), the law of conservation of angular momentum tells us that Angular momentum before $=$ Angular momentum after $$I_{i} \omega_{i}=I_{f} \omega_{f}$$ Or, since we require $I_{i} / I_{f}$ $$\frac{I_{i}}{I_{f}}=\frac{\omega_{f}}{\omega_{i}}=\frac{0.80 \mathrm{rev} / \mathrm{s}}{0.25 \mathrm{rev} / \mathrm{s}}=3.2$$

          A student stands on a freely rotating platform, as shown in Fig. 10 - 10 . With his arms extended, his rotational frequency is $0.25$ rev/s. But when he draws his arm in, that frequency becomes $0.80$ rev/s. Find the ratio of his moment of inertia in the first case to that in the second.
Because there is no external torque on the system (why?), the law of conservation of angular momentum tells us that
Angular momentum before $=$ Angular momentum after
$$I_{i} \omega_{i}=I_{f} \omega_{f}$$
Or, since we require $I_{i} / I_{f}$
$$\frac{I_{i}}{I_{f}}=\frac{\omega_{f}}{\omega_{i}}=\frac{0.80 \mathrm{rev} / \mathrm{s}}{0.25 \mathrm{rev} / \mathrm{s}}=3.2$$

Added by Purificaci-N F.

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