Question

A figure skater during her finale can increase her rotation rate from an initial rate of 1.14 revolutions every 1.98s to a final rate of 2.94 revolutions per second. If her initial moment of inertia was 4.52kg*m², what is her final moment of inertia?

I need the correct answer in order to give full rating.

Answer 1

The law of conservation of angular momentum states that when no external torque acts on an body, there is no change of angular momentum.

$L1=L2$

$I_{1}\cdot\omega_{1}=I_{2}\cdot\omega_{2}$

The final moment of inertia would be:

$\frac{I_{1}\cdot\omega_{1}}{\omega_{2}}=I_{2}$

Substituting values it yields:

$\frac{4.52 kg\cdot m^{2}\cdot\frac{1.14}{1.98}rps}{2.94 rps}=I_{2}$

${\color{Red} 0.88 kg\cdot m^{2}=I_{2}}$