Explanation Given: 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 I = ∫ 0 M r 2 d m Calculation: Consider a solid cylinder shown in given figure: Central axis ⇒ z − a x i s Moment of inertia about central axis = I z Length = H Mass = M Density= mass volume ⇒ ρ = M π R 2 H Consider mass of the small element d m ρ = d m d ( π r 2 H ) ⇒ d m = ρ ( 2 π r H d r ) = M π R 2 H ( 2 π r H d r ) = M R 2 ( 2 r d r

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.5, Problem 45E

To determine

To prove:

The formula for the given cylinder $I_{z} = \frac{1}{2} M R^{2}$

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Chapter 16.5, Problem 44E

Chapter 16.5, Problem 46E

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Chapter 16 Solutions

Calculus - Standalone book

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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To prove: The formula for the given cylinder I z = 1 2 M R 2

Solution Summary: The author explains the formula for the given cylinder, Moment of Inertia I z = 1 2 M R 2.

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To prove:

The formula for the given cylinder $I_{z} = \frac{1}{2} M R^{2}$

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Chapter 16 Solutions

To prove: The formula for the given cylinder I z = 1 2 M R 2

Solution Summary: The author explains the formula for the given cylinder, Moment of Inertia I z = 1 2 M R 2.

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To prove: The formula for the given cylinder Iz=12MR2

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Chapter 16 Solutions

To prove:

The formula for the given cylinder $I_{z} = \frac{1}{2} M R^{2}$