As a physics demonstration, you want a special bowling ball made to demonstrate exactly 1 kg·m2,...

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 25.5 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.

Expert Solution

let r be the radius and m is the mass then the moment of inertia of a solid sphere is I = 2mr² / 5

1 = 2/5 * ( 6.93 * r²) 1 pound = 0. 45 kg

r = 0.6 m 15.4 pounds = 6.93 kg

therefore the diameter should be d=2r = 1.2 m

genius_generous answered 1 year ago

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