Question

A figure skater spins with her arms outstretches at a rate of 10 rev/s. When she pulls her arms closer to her body, her moment of inertial about the spin axis decreased by 10%, what is the skaters new rotational rate in rev/sec?

Answer 1

Angular velocity x rotational inertia = constant

$\omega$ x R = C

Let's just call the original value for $\omega$ 100%, since we don't have an actual value

We are given an R of 10 rev/sec.

so

100% x 10 = C

and we are also told that

10% x R = C

We reduced the original 100% by multiplying by 10%, so we must divide the original value for R by the same factor

to keep C the same

R = 10 / 0.10 = 100 rev/sec