Explanation Given Information: The particle moves along the spiral with the relation r θ 2 = b . That θ ˙ is constant and denoting this constant by ω . Calculation: Differentiate θ ˙ with respective to θ , θ ¨ = 0 Write the particle moves along the spiral with the relation: r θ 2 = b r = b θ 2 (1) Take time derivative for equation (1). r ˙ = 2 b θ 3 θ ˙ (2) Take time derivative for equation (2). r ¨ = 2 b θ 3 θ ¨ + 6 b θ 4 θ ˙ 2 Write the expression for radial component of acceleration ( a r ) : a r = r ¨ − r θ ˙ Substitute 2 b θ 3 θ ¨ + 6 b θ 4 θ ˙ 2 for r ¨ and b θ 2 for r . a r = ( 2 b θ 3 θ ¨ + 6 b θ 4 ) θ ˙ 2 − ( b θ 2 ) θ ˙ = b θ 4 ( − 2 θ θ ¨ + 6 θ ˙ 2 − θ 2 θ ˙ 2 ) Substitute ω for θ ˙ and 0 for θ ¨ . a r = b θ 4 ( − 2 θ ( 0 ) + 6 ω 2 − θ 2 ω 2 ) = b θ 4 ( 6 − θ 2 ) ω 2 Write the expression for transverse component of acceleration ( a θ ) : a θ = r θ ¨ + 2 r ˙ θ ˙ Substitute b θ 2 for r and 2 b θ 3 θ ˙ for r ˙

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 11.5, Problem 11.176P

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The magnitude of the acceleration (a) of the particle in terms of b, θ and θ˙.

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Chapter 11.5, Problem 11.175P

Chapter 11.5, Problem 11.177P

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The magnitude of the acceleration ( a ) of the particle in terms of b , θ and θ ˙ .

Solution Summary: The author calculates the particle's acceleration in terms of b, theta, and stackreldot.

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The magnitude of the acceleration (a) of the particle in terms of b, θ and θ˙.

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Chapter 11 Solutions