Find the moment of inertia of a circular disk of radius R and mass M that...

Find the moment of inertia of a circular disk of radius R and mass M that rotates on an axis passing through its center. [Answer: ½ MR2]
Step 1: Pictorial representation: Sketch a neat picture to represent the situation.

Step 2: Physical representation: 1) Cut the disk into many small rings as it has the circular symmetry. 2) Set up your coordinate system and choose its origin at the pivot point (or the axle location) for convenience. Then choose a not-special piece as a representative of those small masses dm:

Step 3: Determine the moment of inertia of this representative small mass and evaluate the integral for the total moment of inertia:

Step 4: Use the parallel-axis theorem to determine the moment of inertia of the disk around an axis located at the edge of the disk. Then compare the two moments of inertia and explain how the results make sense to you.

Expert Solution

genius_generous answered 8 months ago

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