716_Dynamics 11ed Manual

716_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 21 Problem 21-1 Show that the sum of the moments of inertia of a body, I xx +I yy +I zz , is independent of the orientation of the x , y , z axes and thus depends only on the location of the origin. Solution: I xx I yy + I zz + m y 2 z 2 + d m x 2 z 2 + d + m x 2 y 2 + d + = m m m I xx I yy + I zz + 2 m x 2 y 2 + z 2 + d = m However, x 2 + y 2 + z 2 = r 2 , where r is the distance from the origin O to dm . The magnitude | r | does not depend on the orientation of the x , y , z axes. Consequently, I xx + I yy + I zz is also independent of the
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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