777_Dynamics 11ed Manual

777_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 21 *Problem 21-68 The conical top has mass M , and the moments of inertia are I x = I y and I z . If it spins freely in the ball-and-socket joint at A with angular velocity ω s compute the precession of the top about the axis of the shaft AB . Given: M 0.8 kg = a 100 mm = I x 3.5 10 3 kg m 2 = θ 30 deg = I z 0.8 10 3 × kg m 2 = g 9.81 m s 2 = s 750 rad s = Solution: Using Eq. 21-30. Σ M x I x φ ' 2 sin () cos I z ' sin ' cos ψ ' + + = Guess ' 1 rad s = Given Mg sin aI x ' 2 sin cos I z ' sin ' cos s + + = ' Find ' = ' 1.31 rad s = low precession Guess ' 200 rad s = Given sin x ' 2 sin cos I z ' sin ' cos s + + = ' Find ' = ' 255 rad s =
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