You might have seen basketball showoffs spinning a ball on the tip of a finger. If such a player performs1.91 J of work to set the ball spinning from rest, at what angular speed will the ball rotate? Model abasketball as a thin-walled hollow sphere. For men's basketball, the ball has a circumference of 0.749 mand a mass of 0.624 kgNumberrad/s

Question
Asked Oct 29, 2019
You might have seen basketball showoffs spinning a ball on the tip of a finger. If such a player performs
1.91 J of work to set the ball spinning from rest, at what angular speed will the ball rotate? Model a
basketball as a thin-walled hollow sphere. For men's basketball, the ball has a circumference of 0.749 m
and a mass of 0.624 kg
Number
rad/s
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You might have seen basketball showoffs spinning a ball on the tip of a finger. If such a player performs 1.91 J of work to set the ball spinning from rest, at what angular speed will the ball rotate? Model a basketball as a thin-walled hollow sphere. For men's basketball, the ball has a circumference of 0.749 m and a mass of 0.624 kg Number rad/s

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Expert Answer

Step 1

Consider W, work has been done to set the basketball spinning from the rest. Take the basketball to be thin-walled hollow sphere with moment of inertia(I) with mass(m) and circumference(C).

W 1.91 J
m 0.624 kg
С-0.749 m
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W 1.91 J m 0.624 kg С-0.749 m

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Step 2

Write the formula which relates circumference to the radius(R) and plug the necessary values to find the radius of the basketball.

C = 27R
С
R =
2л
(0.749 m
R =
2(3.14)
R 0.12 m
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C = 27R С R = 2л (0.749 m R = 2(3.14) R 0.12 m

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Step 3

Write the formula for hollow sphere’s moment of inertia through the center of mass an...

2
I mR2
3
2
0.624 kg) (0.12 m)
3
=6x103 kgm2
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2 I mR2 3 2 0.624 kg) (0.12 m) 3 =6x103 kgm2

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Rotational Mechanics

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