Question

the ice skater rotates around its axis, arms outstretched, at an angular velocity $w1=4 rad/s$ . what will be the angular velocity if the slider gathers its hands and at the same time reduces the moment of inertia three times? the system is considered isolated.

Answer 1

Let's assume the angular momentum of the system is conserved. Thus, we have:

$$I_1\omega_1 = I_2\omega_2$$

where $I_1 = 3I_2$ are moments of inertia before and after arms gathering respectively, $\omega_1 = 4rad/s, \omega_2$ are the angular velocities before and after arms gathering respectively. Thus, obtain:

$$\omega_2 = \dfrac{I_1\omega_1}{I_2}=\dfrac{3I_2\omega_1}{I_2} = 3\omega_1\\ \omega_2 = 3\cdot 4rad/s = 12rad/s$$

Answer. 12 rad/s.