Find the moment of inertia of a circular disk of radius R andmass M that rotates on an axis passing through its center. [Answer:½ MR2]
Step 1: Pictorial representation: Sketch a neat picture torepresent the situation.
Step 2: Physical representation: 1) Cut the disk into many smallrings as it has the circular symmetry. 2) Set up your coordinatesystem and choose its origin at the pivot point (or the axlelocation) for convenience. Then choose a not-special piece as arepresentative of those small masses dm:
Step 3: Determine the moment of inertia of this representativesmall mass and evaluate the integral for the total moment ofinertia:
Step 4: Use the parallel-axis theorem to determine the moment ofinertia of the disk around an axis located at the edge of the disk.Then compare the two moments of inertia and explain how the resultsmake sense to you.
