Question

An ice skater spins at $3 \, \pi \, rad \, s^{- 1}$ with her arms extended. If her moment of inertia with arms folded is $75\%$ of that with arms extended, her angular velocity when she folds her arms is

• A. $\pi \, \text{rad s}^{-1}$
• B. $2 \pi \, \text{rad s}^{-1}$
• C. $3 \pi \, \text{rad s}^{-1}$
• D. $4 \pi \, \text{rad s}^{-1}$

Answer 1

Answer: (D)

Here, $\omega_{1} = 3 \pi \, \text{rad s}^{-1} \text{, } \text{I}_{1} = \text{I}$
$\text{I}_{2} = \frac{7 5}{1 0 0} \text{I}_{1} = \frac{3}{4} \text{I, } \omega_{2} = \text{?}$
As $\text{I}_{2} \omega_{2} = \text{I}_{1} \omega_{1}$
$\therefore \omega_{2} = \frac{\text{I}_{1}}{\text{I}_{2}} \times \omega_{1} = \frac{4}{3} \times 3 \pi = 4 \pi \text{ rad s}^{-1}$