Question

A figure skater can increase her spin rotation rate from an initial rate of 1.5 rev every 1.8 seconds to a final rate of 2.9 rev/s. If her initial moment of inertia was 4.35 kg/m² , what is her final moment of inertia?

Answer 1

Let us consider the followings -

I1 = initial moment of inertia = 4.35 kg*m^2
I2 = final moment of inertia = ?
w1= initial rotation rate = 1.5/1.8 = 0.82 rev/s
w2 = final rotation rate = 2.9 rev/s

Apply conservation of angular momentum -

I1 w1 = I2 w2

Put the values-

4.35 x 0.82 = I2 x 2.9

=> I2 = (4.35 x 0.82) / 2.9 = 1.23 kg*m^2

Hence, the final moment of inertia = 1.23 kg*m^2 (Answer)