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 - m^2, so that your students can rotate the ball about its center of mass to get a "feel" for how "big" 1 kg - m^2 is. The bowling ball 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

from the given data

M = 15.4 pounds

= 15.4*0.4536

= 6.985 kg

let R is the required radius.

We know,
Moment of Inertia of a solid sphere, I = (2/5)*M*R^2

R = sqrt(5*I/(2*M))

= sqrt(5*1/(2*6.985))

= 0.598 m

= 59.8 cm

= 59.8/(2.54)

= 23.5 inch

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