A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of 20 rad/s. When she stretches her arms fully, the spinning speed decrease as 10 rad/s. If I is the initial moment of inertia of the dancer, the new moment of inertia is

Question

A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of 20 rad/s. When she stretches her arms fully, the spinning speed decrease as 10 rad/s. If I is the initial moment of inertia of the dancer, the new moment of inertia is (A) 2I (B) 3I (C) I/2 (D) I/3

Tardigrade Admin · Accepted Answer

Here, angular momentum is conserved. Initial angular momentum = Final angular momentum I × 20 = I' × 10, where I' is new moment of inertia ∴ I' = 2I

$2 I$

$3 I$

$I /2$

$I /3$

Here, angular momentum is conserved.
Initial angular momentum = Final angular momentum
$I \times 20 = I^{'} \times 10$ , where $I^{'}$ is new moment of inertia
$∴ I^{'} = 2 I$

Q. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of 20rad/s. When she stretches her arms fully, the spinning speed decrease as 10rad/s. If I is the initial moment of inertia of the dancer, the new moment of inertia is

2I

3I

I/2

I/3

Here, angular momentum is conserved. Initial angular momentum = Final angular momentum I×20=I′×10, where I′ is new moment of inertia ∴I′=2I

$2 I$

$3 I$

$I /2$

$I /3$

Here, angular momentum is conserved.
Initial angular momentum = Final angular momentum
$I \times 20 = I^{'} \times 10$ , where $I^{'}$ is new moment of inertia
$∴ I^{'} = 2 I$