Explanation Calculation: Sketch the cross section of circular cylinder as shown in Figure 1. Express the moment of inertia of circular cylinder about y axis as shown below: I y = 1 2 m a 2 Find the moment of inertia about x and z axis by using parallel axis theorem. I x = I z I x = I z = 1 12 m ( 3 a 2 + h 2 ) + m ( h 2 ) 2 = 1 12 m ( 3 a 2 + h 2 ) + m h 2 4 = m 12 ( 3 a 2 + h 2 + 3 h 2 ) = m 12 ( 3 a 2 + 4 h 2 ) As the symmetry implies I x = I y z = I z x = 0 Consider the point A lie in the y z plane. λ O A = 1 h 2 + a 2 ( h j+ak ) Refer to Equation 9.46 in section, “9.6A mass Product of inertia” in the textbook. The mass products of inertia equal to zero. I O L = I x λ x 2 + I y λ y 2 + I z λ z 2 − 2 I x y λ x λ y − 2 I y z λ y λ z − 2 I z x λ z λ y = I x λ x 2 + I y λ y 2 + I z λ z 2 (1) Substitute 0 for I <

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.6, Problem 9.164P

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Find the mass moment of inertia of the cylinder with respect to the line joining the origin O.

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Chapter 9.6, Problem 9.163P

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Find the mass moment of inertia of the cylinder with respect to the line joining the origin O .

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