In this worksheet, we will practice calculating the moment of inertia of a system given the rotational motions of its components.

**Q2: **

Calculate the moment of inertia of a skater given the following information.

The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius.

The skater with arms extended is approximated by a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.

**Q3: **

A solid sphere of radius 10 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its centre of mass starts from the position shown in the following figure with speed 15 cm/s. What is the maximum angle that the diameter makes with the vertical?

- A
- B
- C
- D
- E

**Q4: **

A rod and a sphere are combined to form a system. The rod’s length is 0.50 m and its mass is 2.0 kg. The sphere’s radius is 20.0 cm and its mass is 1.0 kg. The system can rotate either about the point , at the opposite end of the rod to the sphere, or about the point , where the rod and the sphere connect, as shown in the diagram.