As a physics demonstration, you want a special bowling ball made to demonstrate

Question

As a physics demonstration, you want a special bowling ball made to demonstrate exactly 1 kg . m2, so that your students can rotate the ball about its center of mass to get a "feel" for how "big" 1 kg . m2 is. The bowling balls most familiar to your students has a weight of 15.4 pounds and have a circumference of 26.6 inches, but do not have a moment-of-inertia equal to 1 kg . m2. Since the sporting goods manufacturer has no understanding of how "big" 1 kg . m2 is, calculate the diameter of the demo bowling ball (in inches) it will need to manufacture. Assume that bowling balls are solid, with a constant density.

Explanation / Answer

For a solid spherical ball moment of inertia is equal to 2/5 * M * R^2 we need this equal to 1 kg.m^2 Hence 1 = 2/5 * (15.4*0.45) * R^2 ( Note that 1 pound = 0.45 kg) From here, R = 0.6 m = 23.65 inches

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