729_Dynamics 11ed Manual

# 729_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Engineering Mechanics - Dynamics Chapter 21 inertia of the assembly about the z axis. Given: W p 5lb = W r 3lb = h 1.5 ft = a 0.5 ft = Solution: Lh 2 a 2 + a 2 + = θ acos h L = I z 4 1 3 W r L 2 sin () 2 1 12 W p 2 a 2 2 a 2 + + = I z 0.0881 slug ft 2 = Problem 21-21 If a body contains no planes of symmetry , the principal moments of inertia can be determined mathematically. To show how this is done, consider the rigid body which is spinning with an angular velocity ω , directed along one of its principal axes of inertia. If the principal moment of inertia about this axis is I , the angular momentum can be expressed as H = I ω = I x i + I y j + I z k . The components of H may also be expressed by Eqs. 21-10, where the inertia tensor is assumed to be known. Equate the i , j , and k components of both expressions for H and consider x , y , and z to be unknown. The solution of these three equations is obtained provided the determinant of the
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