Explanation Calculation: Consider v i is velocity of particle with respect to a frame OXYZ . Consider r i is position vector of particle with respect to a frame OXYZ . Consider r ′ i is position vector of particle with respect to a frame A x ′ y ′ z ′ . Consider v ′ i is velocity of particle with respect to a frame A x ′ y ′ z ′ . Express the velocity of particle with respect to a frame OXYZ . v i = v A + v ′ i Express the angular momentum using the relation as follows: H A = ∑ i = 1 n r ′ i × m i v i (1) Substitute v A + v ′ i for v i in Equation (1). H A = ∑ i = 1 n r ′ i × m i ( v A + v ′ i ) = ∑ i = 1 n r ′ i × m i v A + ∑ i = 1 n r ′ i × m i

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 14.29P

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Check and show that HA=H′A at any instant when the condition “A has zero velocity with respect to Newtonian frame Oxyz” must be satisfied at that instant.

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Chapter 14.1, Problem 14.28P

Chapter 14.1, Problem 14.30P

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Check and show that H A = H ′ A at any instant when the condition “ A has zero velocity with respect to Newtonian frame O x y z ” must be satisfied at that instant.

Solution Summary: The author explains how to express the angular momentum using the relation as follows: v_i is velocity of particle with respect to a frame OXYZ.

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Check and show that HA=H′A at any instant when the condition “A has zero velocity with respect to Newtonian frame Oxyz” must be satisfied at that instant.

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Chapter 14 Solutions