Explanation Given Information: The three dimensional motion of a particle is defined by the position vector r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k . Calculation: Write three-dimensional motion of particle in term of position vector equation. r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k Write the expression for velocity using the relation: v = d r d t Substitute ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k for r . v = d ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k d t = R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k Write the expression for acceleration using the relation: a = d v d t Substitute R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k for v . a = d ( R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k ) d t = R ( − ω n sin ω n t − ω n sin ω n t − ω n 2 t cos ω n t ) i + R ( 2 ω n cos ω n t − ω n 2 t sin ω n t ) k = ω n R ( − ( 2 sin ω n t + ω n t cos ω n t ) i + ( 2 cos ω n t − ω n t sin ω n t ) k ) (1) Calculate the velocity ( v ) of the particle. v 2 = v x 2 + v y 2 + v z 2 Substitute R ( cos ω n t − ω n sin ω n t ) for v x , c for v y and R ( sin ω n t + ω n t cos ω n t ) for v z

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 11.5, Problem 11.151P

To determine

The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

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Chapter 11.5, Problem 11.150P

Chapter 11.5, Problem 11.152P

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Chapter 11 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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The radius ( ρ ) of curvature of the path described by the particle when time ( t ) is 0 sec.

Solution Summary: The author describes the three-dimensional motion of a particle defined by the position vector r=(rho ).

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The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

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Chapter 11 Solutions