Dynamics_Part70

Dynamics_Part70 - Problem Set 9: Problem 5. Problem: A thin...

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Unformatted text preview: Problem Set 9: Problem 5. Problem: A thin disk of mass m and radius R spins at constant angular velocity about an axis that passes through its center, Point O. The axis is supported by a housing, which is attached to a horizontal rod that rotates at constant angular velocity as shown. Determine the couple, M, that represents the dynamic reaction at support plate A. Solution: To solve, we work in a coordinate system rotating about the x axis with = i. In this reference frame, the disk rotates about the z axis with = k, and the angular momentum about the disk's center, Point O, is HO = [I] where the disk's inertia tensor is [I] = 1 2 4 mR 1 2 4 mR 0 0 0 1 mR2 4 0 Thus, we find HO = 0 0 0 0 1 2 2 mR 0 1 0 = mR2 k 2 1 2 2 mR 0 1 mR2 4 0 The absolute rate of change of HO is given by the Coriolis Theorem, i.e., 0 0 0 0 = 1 mR2 2 d HO 1 1 dHO = + HO = mR2 k + i mR2 k dt dt 2 2 Now, is constant and i k = -j, wherefore 1 HO = - mR2 j 2 Finally, the couple, M, is equal to HO . Therefore, we conclude that 1 M = - mR2 j 2 ...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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