Explanation Given information: The total mass ( m ) of the system is 300 g. The radius of gyration ( k x ) of assembly is 75 mm . The length ( b ) of bearing is 125 mm. The angular velocity ( ω 1 ) of the bearing is 1,800 rad/s. The angular velocity ( ω 2 ) of the motor casting is ( 0.6 rad/s ) j . Calculation: Write the vector form of angular velocity ( ω ) . ω = ω 1 i + ω 2 j Write the equation of the mass moment of inertia ( I x ) . I x = m k x 2 Write the equation of angular momentum ( H G ) . H G = I x ω 1 i + I y ω 2 j Write the angular velocity of reference frame ( Ω ) . Ω = ω 2 j The angular velocity ( H ˙ G ) G x y z about the reference frame is 0. Write the equation of rate of change of angular momentum ( H ˙ G ) of the system. ( H ˙ G ) = ( H ˙ G ) G x y z + Ω × H G Substitute 0 for ( H ˙ G ) G x y z , ω 2 j for Ω , and I x ω 1 i + I y ω 2 j for H G . ( H ˙ G ) = 0 + ( ω 2 j ) × ( I x ω 1 i + I y ω 2 j ) = − I x ω 1 ω 2 k + 0 = − I x ω 1 ω 2 k (1) Write the equation of the moment of the system. M = b i × B Substitute ( B y j + B z k ) for B. M = b i × ( B y j + B z k ) = − b B z j + b B y k (2) The acceleration of the mass center is negligible. M = H ˙ G Substitute − b B z j + b B y k for M and − I x ω 1 ω 2 k for H ˙ G

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 18.2, Problem 18.79P

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Find the dynamic reactions at A and B.

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Find the dynamic reactions at A and B .

Solution Summary: The author explains the dynamic reactions at A and B. The total mass of the system is 300 g.

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