Concept explainers
Show that the sum of the moments of inertia of a body, Ixx + Iyy + Izz, is independent of the orientation of the x, y, z axes and thus depends only on the location of the origin.
Show that the sum of moments of inertia of a body,
Answer to Problem 1P
The given equation is proved.
Explanation of Solution
Given:
The moment of inertia of a body with respect to
The moment of inertia of a body with respect to
The moment of inertia of a body with respect to
Conclusion:
Express the summation of moments of inertia of body with respect to
Here, the distance from the origin to
Since the distance
Hence, the given expression is satisfied and proved.
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Chapter 21 Solutions
Engineering Mechanics: Dynamics (14th Edition)
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- Find the moment of inertia for the cross-sectional shape about the x and y axes, given the function: y = 2·x2 and L = 1.6 m.arrow_forwardDetermine the moments of inertia with respect to the centroidal axes of the following figure: 30 cm 15 cm 15 cm 7.5 cm 10 cm 10 cm Xarrow_forwardThe product of inertia of area with respect to x-y axes: O Is always positive. O Is always zero. O Can be positive or negative, but it is never zero. O Can be positive, negative, or zero.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L