# 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.

**Q2: **

A skater is spinning on the spot. The skater has a mass of 60.0 kg and can be approximated as a uniform cylinder of radius 0.110 m.

Calculate the moment of inertia of the skater.

The skater extends her arms, and in this configuration her body can be approximated as a cylinder of mass 52.5 kg and radius 0.110 m. From the surface of this cylinder her arms project in opposite directions and perpendicularly to the cylinder’s surface. Each arm can be modelled as 0.900 m long cylinder of mass 3.75 kg. Calculate the moment of inertia of the skater in this configuration.

**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.

Find the moment of inertia of the system about the point .

Find the moment of inertia of the system about the point .

**Q7: **

How do shear stresses and normal stresses differ?

- ANormal stresses act at the surfaces of materials, whereas shear stresses act within materials.
- BShear stresses are the absolute stresses, whereas normal stresses have been divided by the total stress.
- CNormal stresses act within materials, whereas shear stresses act at the surfaces of materials.
- DThey have different units.
- EShear stresses act to slide parallel planes of material apart without changing separation, whereas normal stresses act to increase or decrease the separation between parallel planes of material.

**Q12: **

Which of the following is consistent with the parallel axis theorem for the mass moment of inertia?

- The mass moment of inertia of an object about an axis through the center of mass is smaller than that about any other axis in the same direction.
- The mass moments of inertia of an object about any parallel axes are identical.
- The mass moment of inertia of an object about an axis () is equal to the moment about an axis () through the center of mass plus the mass times the square of the distance from () to ().
- The mass moment of inertia about parallel axes is proportional to the square of the separation between axes.

- AIII and IV only
- BII only
- CI and III only
- DIII only
- EIV only

**Q15: **

A merry-go-round can be modeled as a solid disk of mass 500 kg and a radius of 2.0 m. A child of mass 25 kg stands at a point on the merry-go-round that is 1.0 m away from its axis of rotation, as shown in the diagram. Find the moment of inertia of the system consisting of the merry-go-round and the child. Give your answer to four significant figures.