As a physics demonAs a physics demonstration, you want a special bowling ball ma

Question

As a physics demonAs 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 15.0 pounds and have a circumference of 26.3 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.stration, 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 15.0 pounds and have a circumference of 26.3 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

Since the bowling ball is considered to be a solid sphere, Moment of inertia is I = 2/5 MR^2

Given, I = 1 kg m2

Given Mass = 15 pounds = 6.8 kg

So,

1 = 2/5* 6.80 * r^2

r^2 = 0.3676

r = 0.6063 m

The Diameter of the bowling ball should be

D = 2*r = 1.2126 m = 47.74 inches

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