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.


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 6 0 above the horizontal, what is the speed of the tip of the rod as it passes the horizontal position?


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.


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 8 . 9
  • B 7 . 9
  • C 1 1
  • D 1 0
  • E 1 2


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