Problem 10.58 A ball of mass M and radius r 1 on the end of a thin massless rod

Question

Problem 10.58

A ball of mass M and radius r1 on the end of a thin massless rod is rotated in a horizontal circle of radius R0 about an axis of rotation AB, as shown in the figure(Figure 1) .

Part B

Using the parallel-axis theorem and considering the finite radius of the ball, calculate the moment of inertia of the ball about AB.

Express your answer in terms of the given quantities.

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The correct answer does not depend on: mR, mR0.

Part C

Calculate the percentage error introduced by the point mass approximation for r1 = 7.5cm and R0 = 1.3m .

Express your answer using two significant figures.

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Figure 1 of 1

Explanation / Answer

b)I about centre of ball=2/5*Mr1^2
I about AB by parallel axis thm=2/5Mr1^2+M*R0^2
c)I=1.69225M
and considering point mass,I=MR0^2=1.69M
thus error=(1.69225-1.69)M=0.00225M
and error %=(0.00225M/1.69225M)*100 %=0.13 %.Ans

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