Question

A wooden disc of 2 m radius and 120 kg mass rotates through a vertical axis at the

centre of the disc. Later a 100 kg bag containing sand is released vertically onto the disc

at a point near the side of the disc. (o = 3 rad s-1)

Calculate the

(a) moment of inertia of the disc. [3 m]

(b) angular velocity after the sand bag is released (assume that the sand bag is a

particle).

Answer 1

(a) The moment of inertia of the empty disk:

$$I=\frac12 MR^2=240\text{ kg m}^2.$$

(b) Apply angular momentum conservation:

$$L_i=L_f,\\ I\omega_0=(I+I_b)\omega,\\\space\\ \omega=\omega_0\frac{I}{I+I_b}=\omega_0\frac{I}{I+mR^2}=1.125\text{ rad/s}.$$