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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 9 / Problem 40E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Answer: A hollow spherical shell has mass 8.20 kg and

Chapter 9, Problem 40E

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QUESTION:

Problem 40E

A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s2. What is the kinetic energy of the shell after it has turned through 6.00 rev?

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QUESTION:

Problem 40E

A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s2. What is the kinetic energy of the shell after it has turned through 6.00 rev?

ANSWER:

Solution 40E

Step 1:

Data given

Mass of the spherical shell $M\ =\ 8.20\ kg\$

Radius $R=\ 0.220\ m$

Acceleration $\alpha{}=\ 0.890\ rad/{s}^{2}$

Revolution $\theta{}=6.00\ rev=37.{6}^{\ }\ rad\ \$

We shall find the inertia of the spherical shell

It is given by

$I=\ (2/3)\ M{R}^{2}$

Substituting values we get

$I=\ (2/3)\times{}\ 8.20\ kg\times{}(0.220\ m{)}^{2}$

$I=0.26\ kg\ {m}^{2}$

Hence we have inertia as $0.26\ kg\ {m}^{2}$

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