Question

A computer disk drive is turned on starting from rest and has constant angular acceleration.

- If it took 0.830 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?

- What is its angular acceleration, in rad/s2?

A uniform, solid disk with mass m and radius R is pivoted about a horizontal axis through its center. A small object of the same mass m is glued to the rim of the disk.

- If the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when the small object is directly below the axis.

Express your answer in terms of the variables m, R, and appropriate constants.

Answer 1

1.

angular acceleration

x = 0.5 at^2

2 * 2* 3.14 = 0.5* a * 0.83^2

a = 36.46 rad/s^2

using 1st equation of motion

2* 3.14 = 0. 5* 36.46* t^2

t = 0.587 s

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b)

angular acceleration = 36.46 rad/s^2

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2.

usinh conservation of energy

mg R = 0.5 m v^2 + 0.5 Iw^2

mgR = 0.5 m R^2 w^2 + 0.5* 0.5* m R^2 w^2

g = ( 0.5 + 0.25) Rw^2

w = sqrt ( 4 g / 3R)

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