An ice skater spins at 3 π 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

Question

An ice skater spins at 3 π 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) π textrad s-1 (B) 2 π textrad s-1 (C) 3 π textrad s-1 (D) 4 π textrad s-1

Tardigrade Admin · Accepted Answer

Here, ω1 = 3 π textrad s-1 text, textI1 = textI textI2 = (7 5/1 0 0) textI1 = (3/4) textI, ω2 = text? As textI2 ω2 = textI1 ω1 ∴ ω2 = ( textI1/ textI2) × ω1 = (4/3) × 3 π = 4 π text rad s-1

Q. An ice skater spins at $3 π r a d s^{- 1}$ 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

$π rad s^{- 1}$

$2 π rad s^{- 1}$

$3 π rad s^{- 1}$

$4 π rad s^{- 1}$

Here, $ω_{1} = 3 π rad s^{- 1}, I_{1} = I$
$I_{2} = \frac{75}{100} I_{1} = \frac{3}{4} I, ω_{2} = ?$
As $I_{2} ω_{2} = I_{1} ω_{1}$
$∴ ω_{2} = \frac{I _{1}}{I _{2}} \times ω_{1} = \frac{4}{3} \times 3 π = 4 π rad s^{- 1}$

Q. An ice skater spins at 3πrads−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

πrad s−1

2πrad s−1

3πrad s−1

4πrad s−1