Physics 1120 In-Class Problems: Moment of Inertia

1. The moment of inertia of an oxygen molecule about an axis through the centre of mass and perpendicular to the line joining the atoms is 1.95 × 10^-46 kg-m². The mass of an oxygen atom is 2.66 × 10^-26 kg. What is the distance between the atoms? Treat the atoms as particles.

2. An empty beer can has a mass of 50 g, a length of 12 cm, and a radius of 3.3 cm. Assume that the shell of the can is a perfect cylinder of uniform density and thickness.
   (a) What is the mass of the lid/bottom?
   (b) What is the mass of the shell?
   (c) Find the moment of inertia of the can about the cylinder's axis of symmetry.
   

3. A dumbbell consists of two uniform spheres of mass M and radius R joined by a thin rod of mass m, length L, and radius r (see diagram).
   (a) What is the moment of inertia about the centre of mass and perpendicular to the rod (Axis A)?
   (b) About an axis through one sphere and perpendicular to the rod (Axis B)?
   (c) About an axis along the rod (Axis C)?
   
   

4. A hole of radius r has been drilled in a flat, circular plate of radius R. The centre of the hole is at a distance d from the centre of the circle. The mass of the complete body was M. Find the moment of inertia for rotation about an axis through the centre of the plate.
   

5. A thick spherical shell has an inner radius R₁, an outer radius R₂, and a mass M. The material that the spherical shell is made of is uniform. Find the moment of inertia of the thick shell about an axis through the centre of the sphere. The volume of a sphere is 4πr³/3.
   

6. The object shown in the diagram below consists of a 100-kg, 25.0 cm radius cylinder connected by four 5.00-kg, 0.75-m long thin rods to a thin-shelled outer cylinder of mass 20.0 kg. A small chunk of metal of mass 1.00 kg has been welded to the outer cylinder. What is the moment of inertia of the object about the centre of the inner cylinder? Treat the metal chunk as a point mass.
   

7. The object in the diagram below consists of five thin cylinders arranged in a circle. A thin disk has been welded to the tops and the bottoms of the cylinders. The cylinders each have a mass of 250 g, a length of 15.0 cm, and a radius of 1.00 cm. The disks are each 125 g and have a radius of 5.00 cm. Find the moment of inertia of the whole object about an axis through the centres of the disks.
   

Problems: Chapter 8 - #18,22

Questions? mike.coombes@kwantlen.ca