Explanation 1) Concept: We can find the rotational inertia of the two spheres about an axis through its center using the corresponding formula. Then using the formula for torque in terms of M.I, we can find the magnitude of torque required to bring the smaller sphere and larger sphere from rest to an angular speed of 317 r a d / s i n 15.5 s . We can find the average force on them using the relation between torque and force. 2) Formulae: i) I s p h e r e = 2 5 m R 2 ii) τ = I α iii) F = τ r 3) Given: i) Mass of each uniform solid sphere is, m = 1.65 k g . ii) Radius of one smaller sphere is, r = 0.226 m iii) Radius of one larger sphere is, R = 0.854 m 4) Calculations: M.I of the larger sphere is I l = 2 5 m R 2 = 2 5 1.65 0.854 2 = 0.4813 k g . m 2 M.I of the smaller sphere is I s = 2 5 m r 2 = 2 5 1.65 0.226 2 = 0.0337 k g . m 2 We know that τ = I α But, α = ω f - ω i t Hence, τ = I ω f - ω i t a) Torque on the smaller sphere is τ = 0

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 10, Problem 68P

To determine

To find:

a) The magnitude of torque required to bring the smaller sphere from rest to an angular speed of 317radsin 15.5 s.

b) The magnitude of force that must be applied tangentially at the smaller sphere’s equator to give the torque.

c) The value of torque for the larger sphere.

d) The value of force for the larger sphere.

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Chapter 10, Problem 67P

Chapter 10, Problem 69P

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Solution Summary: The author explains how to find the magnitude of torque required to bring the smaller sphere from rest to an angular speed of 317radsin15.5s.

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