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 middot m^2, so that your students can rotate the ball about its center of mass to get a "feel" for how "big" 1 kg middot m^2 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 middot m^2. Since the sporting goods manufacturer has no understanding of how "big" 1 kg middot m^2 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. 8.4055

Explanation / Answer

for solid sphere, moment of inertia =0.4*mass*radius^2

mass given=weight/g

=15.4*4.44822 N/9.8 m/s^2

=7 kg

so using moment of inertia of 1 kg.m^2,

1=7*radius^2

==>radius=sqrt(1/7)=0.378 m

diameter required=2*radius=2*0.378 m=29.76 inches

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