Explanation Given: Sphere of radius R of total mass M with uniform mass density about any axis passing through the center of the sphere. The mass density of the sphere is δ = M 4 3 π R 3 Key points: • Moment of Inertia is the sum of the products of the mass of the each particle in the body with the square of distance from the axis of rotation Calculation: Consider a sphere as shown in figure: radius = R mass = M mass density= δ = M 4 3 π R 3 Moment of inertia of thin disk of small mass d m ⇒ d I = 1 2 y 2 d m = 1 2 y 2 δ d v = 1 2 y 2 δ π y 2 d z Integrating the moment of inertia of small element

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 16.5, Problem 45E

To determine

To prove:

The moment of inertia of sphere is $\frac{2}{5} M R^{2}$ .

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Chapter 16.5, Problem 44E

Chapter 16.5, Problem 46E

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Chapter 16 Solutions

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To prove: The moment of inertia of sphere is 2 5 M R 2 .

Solution Summary: The author explains the moment of inertia of sphere of radius R of total mass M with uniform mass density about any axis passing through the center.

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To prove:

The moment of inertia of sphere is $\frac{2}{5} M R^{2}$ .

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Chapter 16 Solutions

To prove: The moment of inertia of sphere is 2 5 M R 2 .

Solution Summary: The author explains the moment of inertia of sphere of radius R of total mass M with uniform mass density about any axis passing through the center.

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Chapter 16 Solutions

To prove:

The moment of inertia of sphere is $\frac{2}{5} M R^{2}$ .