Solved: Moment of Inertia An annular cylinder has an inside radius of and an outside

Chapter 13, Problem 57

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An annular cylinder has an inside radius of \(r_{1}\) and an outside radius of \(r_{2}\) (see figure). Its moment of inertia is \(I=\frac{1}{2} m\left(r_{1}^{2}+r_{2}^{2}\right)\), where m is the mass. The two radii are increasing at a rate of 2 centimeters per second. Find the rate at which I is changing at the instant the radii are 6 centimeters and 8 centimeters. (Assume mass is a constant.)

Text Transcription:

r_1

r_2

I=frac12m(r_1^2+r_2^2)

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