Explanation Calculation: Find the position vector of OA . O A → = 3 2 a i − 3 a j + 3 a k Find the magnitude of O A → using the relation as shown below: d O A = ( 3 2 a ) 2 + ( − 3 a ) 2 + ( 3 a 2 ) = ( 9 4 a 2 ) + ( 9 a 2 ) + ( 9 a 2 ) = 3 a 1 + 4 + 4 4 = 3 a 9 4 = 3 a 3 2 d O A = 9 a 2 Find the magnitude of λ O A as shown below: λ O A = 1 9 2 a ( 3 2 a i − 3 a j+3 a k ) = 2 9 a ( 3 2 a i − 3 a j+3 a k ) = 1 3 ( i − 2 j + 2 a k ) For a rectangular coordinate system with origin at point A and axes aligned with the given x , y , z axes. Refer to Figure 9.28 in section,”9.5E Moments of inertia of composite bodies” in the textbook. Express the moment of inertia about x and z axis of circular cone as shown below: I x = I z = 3 5 m [ 1 4 a 2 + ( 3 a ) 2 ] = 3 5 m [ 1 4 a 2 + 9 a 2 ] = 3 5 m [ 37 a 2 4 a 2 ] = 111 20 m a 2 Express the moment of inertia about y axis of circular cone as shown below: I y = 3 10 m a 2 As the symmetry implies I x y = I y z = I z x = 0 . Refer to Equation 9.46 in section, “9

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ISBN: 9781259977244

Author: BEER

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Moment of Inertia

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 9.163P

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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Chapter 9.6, Problem 9.162P

Chapter 9.6, Problem 9.164P

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A .

Solution Summary: The author calculates the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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