Question

A ballerina is performing a solo for The Nutcracker. Halfway through, she begins to spin at 0.5rev/s on her toes with her arms stretched out from her sides, with a moment of inertia of 1.9kgm2. She then pulls her arms to her chest, spinning at 1.3rev/s.

1. What is her moment of inertia when she brings her arms to her chest? (Hint: You may leave the angular velocities in the units given of revolutions/second. Whether you keep them this way or convert them to radians/second, you should get the same final answer.)

2. What is her angular momentum? (Hint: By conservation of angular momentum, your initial angular momentum should equal your final, so you only need to find either her initial or final. Whichever you choose, change your angular velocity from revolutions/second to radians/second. 1rev = 2π radians.)

Answer 1

What is her moment of inertia when she brings her arms to her chest?

use conservation of angular momentum

I_i w_i = I_f w_f

1.9 * 0.5 = I_f * 1.3

I_f = 0.731 Kg.m²

__________________

What is her angular momentum?

L = Iw

where w = 0.5 rev/sec = 0.5 * 2 * pi = 3.1415 rad/sec

so,

L = 5.97 Kg,m² / s