When a skater pulls her arms in, it reduces her moment of inertia from 2.12 kg•m2 to 0.699 kg•m2. If she was initially spinning 3.25 rad/s, what is her final angular velocity?

Question



Answer 1

Inertia and angular velocity relate to the calculation of angular momentum. As in linear momentum (P), angular momentum (L) is also a conserved quantity (you can't just lose it but can transform it into something else).

L = Iω

And due to conservation --> L_initial = L_final

I_initial = 2.12 kg/m^2

ω_initial = 3.25 rad/s

I_final = 0.699 kg/m^2

ω_final = ???

2.12 kg/m^2 * 3.25 rad/s = 0.699 kg/m^2 * ω_final

Now solving for ω_final = 2.12 * 3.25 / 0.699 = 9.86 rad/s. (significant figure rounding)