Explanation According to problem 11.95 r = ( R t c o s ω n t ) i + c t j + ( R t s i n ω n t ) k The normal acceleration a n is defined as: a n = v 2 ρ Where, ρ - Radius of curvature The first derivative of motion is equal to velocity, v = d x d t The first derivative of velocity is equal to acceleration, a = d v d t Calculation: According to given information, r = ( R t c o s ω n t ) i + c t j + ( R t s i n ω n t ) k Differentiate to find velocity, v = d r d t = R ( c o s ω n t − ω n t s i n ω n t ) i + c j + R ( s i n ω n t + ω n t c o s ω n t ) k Differentiate to find acceleration a = d v d t = R ( − ω n s i n ω n t − ω n s i n ω n t − ω n 2 t c o s ω n t ) i + R ( ω n c o s ω n t + ω n c o s ω n t − ω n 2 t s i n ω n t ) k Solve and rearrange, a = ω n R [ − ( 2 s i n ω n t + ω n t c o s ω n t ) i + ( 2 c o s ω n t − ω n t s i n ω n t ) k ] Now find v 2

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

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

Publisher: McGraw-Hill Education

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Chapter 11.5, Problem 11.151P

To determine

The radius of curvature.

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Chapter 11.5, Problem 11.150P

Chapter 11.5, Problem 11.152P

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The radius of curvature.

Solution Summary: The author explains the radius of curvature. The first derivative of motion is equal to velocity.

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