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Unformatted text preview: 8.6. CHAPTER 8, PROBLEM 6 333 8.6 Chapter 8, Problem 6 Problem: A thin square plate of side a and mass m is hinged at Points A and B to a clevis, which rotates with constant angular velocity ω = ω j . The components of the moment of inertia tensor for the center-of-mass based principal axis system of the disk ( x I , y I , z I ) are I Gx I = I Gz I = 1 12 ma 2 and I Gy I = 1 6 ma 2 Also, the center of mass lies at x I = 1 2 a , y I = z I = 0 . (a) Compute the inertia tensor relative to Point O. (b) Determine the angular-momentum vector relative to Point O, H O . (c) Compute d H O /dt . (d) Find the moment, M O , due to the plate’s weight. (e) Determine the angle β as a function of ω , a and g , the acceleration of gravity. Solution: The first thing we must do is take care of kinematical considerations. For the problem at hand, we will have to transform from the given xyz coordinates to principal axis coordinates x I y I z I . The figure below illustrates the relation between the xyz and x I y I z I coordinate systems (the z and z I axes are aligned).axes are aligned)....
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