Question

A fidget spinner of radius R=0.05m has a moment of inertia l=1.25 x 10^-4 kg m^2 and is rotating at 8.40 rad/s. A large fly whose mass is 0.3 kg lands onto the edge of the rotating spinner. Calculate the angular speed of the system after the fly falling onto the spinner.

Answer 1

To calculate the angular speed of the system after the fly falling onto the spinner, we can apply angular momentum conservation:

$$L_1\omega_1=(L_1+L_f)\omega_2, \\\space\\ L_1\omega_1=(L_1+m_fR^2)\omega_2, \\\space\\ \omega_2=\frac{L_1\omega_1}{(L_1+m_fR^2)\omega_2}=1.02\text{ rad/s}.$$