Worksheet: Moment of Inertia

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

Q1:

A uniform rod of mass 1.0 kg and length 2.0 m is free to rotate about one of its ends, as shown in the accompanying diagram. If the rod is released from rest at an angle of above the horizontal, what is the speed of the tip of the rod as it passes the horizontal position?

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.