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 The moment of inertia about central axis d I z = 1 2 R 2 d m The moment of inertia along x − axis and y − axis equals by symmetry ⇒ d I x = d I y by the perpendicular axes theorem d I z = d I x + d I y d I z = 2 d I x d I x = d I z 2 ⇒ d I x = 1 4 R 2 d m Using parallel axes theorem,the moment of inertia about the x − a x i s

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 16.5, Problem 48E

To determine

To prove:

The formula for the given cylinder $I_{x} = \frac{1}{4} M R^{2} + \frac{1}{12} M H^{2}$

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Chapter 16.5, Problem 47E

Chapter 16.5, Problem 49E

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To prove : The formula for the given cylinder I x = 1 4 M R 2 + 1 12 M H 2

Solution Summary: The author explains the formula for the given cylinder I x = 1 4 M R 2 + 1 12 M H 2

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To prove:

The formula for the given cylinder $I_{x} = \frac{1}{4} M R^{2} + \frac{1}{12} M H^{2}$

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Chapter 16 Solutions

To prove : The formula for the given cylinder I x = 1 4 M R 2 + 1 12 M H 2

Solution Summary: The author explains the formula for the given cylinder I x = 1 4 M R 2 + 1 12 M H 2

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To prove: The formula for the given cylinder Ix=14MR2+112MH2

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Chapter 16 Solutions

To prove:

The formula for the given cylinder $I_{x} = \frac{1}{4} M R^{2} + \frac{1}{12} M H^{2}$