Explanation Given information: Rotor starts from rest at t = 0 . After 10 s , rotor has completed 20 revolutions. First differentiation of angular velocity with respect to time is equal to angular acceleration. α = d ω d t First differentiation of angular coordinate with respect to time is equal to angular velocity. ω = d θ d t Calculation: The angular acceleration α can be given as, α = k t α = d ω d t Therefore, k t = d ω d t Rearrange d ω = k t d t Integrate ∫ 0 ω d ω = ∫ o t k t d t [ ω ] 0 ω = [ k t 2 2 ] 0 t ω = k t 2 2 → ( 1 ) But we know that, ω = d θ d t Therefore, To determine (b) Time required for the rotor to complete its first 40 revolutions.

12th Edition

ISBN: 9781259977237

Author: BEER

Publisher: MCG

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Chapter 15.1, Problem 15.4P

To determine

(a)

Angular velocity at t=20 s.

To determine

(b)

Time required for the rotor to complete its first 40 revolutions.

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Chapter 15.1, Problem 15.3P

Chapter 15.1, Problem 15.5P

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Chapter 15 Solutions

Vector Mechanics For Engineers

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