Example #1: Inertia of disc with point masses

Practice: You build a wheel out of a thin circular hoop of mass 5 kg and radius 3 m, and two thin rods of mass 2 kg and 6 m in length, as shown below. Calculate the system’s moment of inertia about a central axis, perpendicular to the hoop.

Practice: A composite disc is built from a solid disc and a concentric, thick-walled hoop, as shown below. The inner disc (solid) has mass 4 kg and radius 2 m. The outer disc (thick-walled) has mass 5 kg, inner radius 2 m, and outer radius 3 m. Calculate the moment of inertia of this composite disc about a central axis perpendicular to the discs.

Practice: Three small objects, all of mass 1 kg, are arranged as an equilateral triangle of sides 3 m in length, as shown. The left-most object is on (0m, 0m). Calculate the moment of inertia of the system if it spins about the (a) X axis; (b) Y axis.

This problem describes a method of determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. A mass m is suspended by a cord wound around the inner shaft (radius r) of a turntable supporting the object. When the mass is released from rest, it descends uniformly a distance h, acquiring a speed v.
Find moment of inertia of the equipment (including the turntable) in terms of magnitudes of given variables.

Consider a system composed of three thin rods each of mass m and length L that are welded together to form an equilateral triangle. What is the moment of inertia of this triangle for rotation about an axis that is perpendicular to the plane of the triangle and through one of vertices of the triangle? The moment of inertia of a rod rotated about its center of mass is Irod, cm =1/12mL2.
1. 17/12mL2
2.7/3mL2
3.5/6mL2
4.3/2mL2
5.1/2mL2
6.2/3mL2
7.11/12mL2
8. mL2