2. A table tennis bat is made up of a circular disk (diameter \( =0.20 \mathrm{~m}, \mathrm{~m}=0.075 \mathrm{~kg} \) ) and a handle (model as a circular cylinder) of diameter \( 0.015 \mathrm{~m} \), length \( =0.10 \mathrm{~m} \), and mass \( =0.05 \mathrm{~kg} \). Find its moment of inertia about its center of mass.

Step 1 ：Find the moment of inertia of the disk: \( I_{disk} = \frac{1}{2} m_{disk} r_{disk}^2 = \frac{1}{2} (0.075) (0.10)^2 \)

Step 2 ：Find the moment of inertia of the handle: \( I_{handle} = \frac{1}{4} m_{handle} d_{handle}^2 + \frac{1}{12} m_{handle} h_{handle}^2 = \frac{1}{4} (0.05) (0.015)^2 + \frac{1}{12} (0.05) (0.10)^2 \)

Step 3 ：Find the total moment of inertia: \( I_{total} = I_{disk} + I_{handle} \)