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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: Calculate the moment of inertia of each of the

Chapter 9, Problem 31E

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QUESTION:

Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed.

(a) A thin \(2.50-\mathrm{kg}\) rod of length \(75.0 \mathrm{~cm}\), about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it.

(b) A \(\text { 3.00-kg }\) sphere \(38.0 \mathrm{~cm}\) in diameter, about an axis through its center, if the sphere is (i) solid and (ii) a thin-walled hollow shell.

(c) An \(8.00-\mathrm{kg}\) cylinder, of length \(19.5 \mathrm{~cm}\) and diameter \(12.0 \mathrm{~cm}\), about the central axis of the cylinder, if the cylinder is (i) thin-walled and hollow, and (ii) solid.

Equation Transcription:

Text Transcription:

2.50-kg

75.0 cm

3.00-kg

38.0 cm

8.00-kg

19.5 cm

12.0 cm

Questions & Answers

QUESTION:

Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed.

(a) A thin \(2.50-\mathrm{kg}\) rod of length \(75.0 \mathrm{~cm}\), about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it.

(b) A \(\text { 3.00-kg }\) sphere \(38.0 \mathrm{~cm}\) in diameter, about an axis through its center, if the sphere is (i) solid and (ii) a thin-walled hollow shell.

(c) An \(8.00-\mathrm{kg}\) cylinder, of length \(19.5 \mathrm{~cm}\) and diameter \(12.0 \mathrm{~cm}\), about the central axis of the cylinder, if the cylinder is (i) thin-walled and hollow, and (ii) solid.

Equation Transcription:

Text Transcription:

2.50-kg

75.0 cm

3.00-kg

38.0 cm

8.00-kg

19.5 cm

12.0 cm

ANSWER:

Solution to 31E

Step 1

(a)

Mass of the rod=2.5kg

Length of the rod =75cm=0.75m

(i)axis passing through one end

I=(⅓)ML2

I=(⅓)(2.5x0.75)

I=0.469kgm2

(ii)Axis through centre of rod

I=(1/12)ML2

I=(1/12)(2.5x0.75)

I=0.117kgm2

(iii)For a very thin rod, since the mass is near to the axis, thus the Moment of Inertia =0

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