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CALC The balance wheel of a watch vibrates with an angular

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 44E Chapter 14

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 44E

CALC The balance wheel of a watch vibrates with an angular amplitude ?, angular frequency ?, and phase angle ? = 0. (a) Find expressions for the angular velocity d?/dt and angular acceleration d2?/dt2 as functions of time. (b) Find the balance wheel’s angular velocity and angular acceleration when its angular displacement is ?, and when its angular displacement is ?/2 and ? is decreasing. (?Hint:? Sketch a graph of ? versus t.)

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Solution 44E The angular displacement of a SHM is given by, = cos(t + )…..(1), where is angular amplitude, is angular frequency and is phase angle. Given that, = 0 Therefore, from equation (1), = cost…..(2) (a) Angular velocity can be calculated by differentiating equation (2) with respect to time d = ()sint dt d dt = sint…..(3) This is the angular velocity as a function of time. Angular frequency can be calculated by differentiating equation (3) with respect to time, 2 2 dt2 = cost…..(4) This is the angular acceleration as a function of time. (b) When angular displacement is , We get from equation (2), = cost cost = 1 Therefore, sint = 0 Using this value in equation (3), we can get angular velocity, d dt = 0 Therefore, angular velocity at displacement is zero. Angular acceleration can be calculated from equation (4) using cost = 1 d 2 dt2 = Therefore, a ngular acceleration a t displacement is .2 When the displacement is 2, From equation (2), 2 = cost cost = 1/2 3 Then, sint = 2 From equation (3), d 3 Angular velocity dt = 2 d = 3 dt 2 3 The required angular velocity is 2 From equation (4), 2 Angular acceleration d 2 = /2 dt This is the required angular acceleration.

Step 2 of 3

Chapter 14, Problem 44E is Solved
Step 3 of 3

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 44E from 14 chapter was answered, more than 310 students have viewed the full step-by-step answer. The answer to “CALC The balance wheel of a watch vibrates with an angular amplitude ?, angular frequency ?, and phase angle ? = 0. (a) Find expressions for the angular velocity d?/dt and angular acceleration d2?/dt2 as functions of time. (b) Find the balance wheel’s angular velocity and angular acceleration when its angular displacement is ?, and when its angular displacement is ?/2 and ? is decreasing. (?Hint:? Sketch a graph of ? versus t.)” is broken down into a number of easy to follow steps, and 73 words. The full step-by-step solution to problem: 44E from chapter: 14 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: angular, acceleration, its, velocity, balance. This expansive textbook survival guide covers 26 chapters, and 2929 solutions.

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CALC The balance wheel of a watch vibrates with an angular