Explanation Calculation: Refer to Equation 14.7 in section 14.1B in the textbook. Express the angular momentum of system of particles. The relation between the angular momentum H o and H G . H o = ∑ i = 1 n ( r i × m i v i ) (1) Here, H o is angular momentum and m i v i is collinear. Substitute ( r ¯ + r ′ i ) for r i in Equation (1). H o = ∑ i = 1 n ( ( r ¯ + r ′ i ) × m i v i ) = ∑ i = 1 n ( r ¯ × m i v i ) + ∑ i = 1 n ( r ′ i × m i v i ) = r ¯ ∑ i = 1 n ( m i v i ) + ∑ i = 1 n ( r ′ i × m i v i ) = r ¯ × m v ¯ + H G Refer to Equation 14.11 in section 14.1B in the textbook. ∑ M o = H ˙ o (2) The resultant the moment resultant about the fixed point o of the external force are equal to the rates changes of linear momentum and H ˙ o respectively

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.1, Problem 14.28P

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Prove the relation ∑MG=HG

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Prove the relation ∑ M G = H G

Solution Summary: The author explains the relation between the angular momentum of system of particles and H_o.

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Prove the relation ∑MG=HG

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