Answer to Question #246930 in Physics for Shirley

Question

Two discs are rotating about an axis as shown in the figure. The moment of inertia

of the right disc is 2 kg m2 and it rotates with angular speed of 2000 rpm. The

moment of inertia of the left disc is 5 kg m2 and it rotates in the opposite direction

with angular speed of 100 rpm. The discs are suddenly clamped together.

Determine the final common angular speed of the clamped discs.

Answer 1

According to angular momentum conservation, we have:

$$L_i=L_f,\\ I_r\omega_r-I_l\omega_l=(I_l+I_r)\omega,\\\space\\ \omega=\frac{I_r\omega_r-I_l\omega_l}{I_l+I_r}=500\text{ rpm}$$

in the direction of initial motion of the right disk.