Engineering Mechanics - DynamicsChapter 21inertia of the assembly about the zaxis.Given:Wp5lb=Wr3lb=h1.5 ft=a0.5 ft=Solution:Lh2a2+a2+=θacoshL⎛⎝⎞⎠=Iz413WrL2sin()2112Wp2a22a2+⎣⎦+=Iz0.0881 slug ft2⋅=Problem 21-21If a body contains no planes of symmetry, the principal moments of inertia can be determinedmathematically. To show how this is done, consider the rigid body which is spinning with an angularvelocity ω,directed along one of its principal axes of inertia. If the principal moment of inertia aboutthis axis is I, the angular momentum can be expressed as H= Iω= Ixi+ Iyj+ Izk. Thecomponents of Hmay also be expressed by Eqs. 21-10, where the inertia tensor is assumed to beknown. Equate the i, j, and kcomponents of both expressions for Hand consider x, y, and zto beunknown. The solution of these three equations is obtained provided the determinant of the
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