Explanation Write the expression to obtain the angular momentum ( H 0 ) . H 0 = I x x ω x i + I y y ω y j + I z z ω z k (I) Here, moments of inertia are I x x , I y y and I z z , angular velocity along x , y and z direction is ω x , ω y and ω z . Conclusion: Write the angular velocity of the rotor about z axis ( p ) . p = 100 k rev / min p = 100 k ( 2 π 60 ) rad / s p = 10 π 3 k rad / s Write the angular velocity of the rotor about x axis ( γ ˙ ) . γ ˙ = − 4 i rad / s Write the angular velocity of the rotor which makes γ with y axis and 90 ° − γ with z axis ( N ) . N = 20 ( cos γ j + sin γ k ) N = 20 ( 3 2 j + 1 2 k ) ( 2 π 60 ) rad / s N = π 3 ( 3 j + k ) rad / s Write the expression to obtain the angular velocity of the rotor ( ω ) . ω = p + γ ˙ + N (II) Substitute 10 π 3 k rad / s for p , − 4 i rad / s for γ ˙ and π 3 ( 3 j + k ) rad / s for N in Equation (II)

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Forced undamped vibrations

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Chapter 7.8, Problem 62P

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The angular momentum of the rotor.

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Chapter 7.8, Problem 61P

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