A figure skater can increase her spin rotation rate from 26 rpm to 165 rpm. Given that her initial moment of inertia is 4.6 kg - m2, find her final moment of inertia.
To find the final moment of inertia of the figure skater, we can use the principle of conservation of angular momentum. Angular momentum is calculated by the equation:
L = Iω
Where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Since the angular momentum is conserved, we can set the initial angular momentum equal to the final angular momentum:
L_initial = L_final
I_initial * ω_initial = I_final * ω_final
Given that the initial angular velocity (ω_initial) is 26 rpm and the final angular velocity (ω_final) is 165 rpm, and the initial moment of inertia (I_initial) is 4.6 kg-m^2, we can rearrange the equation to solve for the final moment of inertia (I_final):
I_final = (I_initial * ω_initial) / ω_final
Substituting the values:
I_final = (4.6 kg-m^2 * 26 rpm) / 165 rpm
Simplify the equation:
I_final = 0.73 kg-m^2
Therefore, the final moment of inertia of the figure skater is 0.73 kg-m^2.