Explanation Consider a centrifuge tube of mass M to be a thin tube with sides a and b Write the equation for moment of inertia I 1 = 1 12 M ( a 2 + b 2 ) (I) Here I 1 is the moment of inertia of the centrifuge tube, M is the mass of the centrifuge tube, a is the length of the tube and b is the width of the tube. If 2 chairs of mass m are mounted on the either side of the tube and 2 astronauts of mass m ' are seated on each chair. The chair–astronaut system can be considered as cube with side R . Write the equation for moment of inertia for cube 1 2 = 2 ( ( ( m + m ' ) R 2 6 ) + ( m + m ' ) d 2 ) (II) Here m is the mass of the chair, m ' is the mass of astronaut, R is the side of the cube and d is the distance from the rotational axis. Write the equation for total moment of inertia. I = I 1 + I 2 = 1 12 M L 2 + 2 ( ( ( m + m ' ) R 2 6 ) + ( m + m ' ) d 2 ) (III) Conclusion: Substitute 3880 kg for M , 18 m for a , 2

4th Edition

ISBN: 9780134988559

Author: Wolfson, Richard

Publisher: Pearson Education,

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Chapter 10, Problem 40E

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Moment of inertia of a given body.

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Chapter 10, Problem 39E

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