A solid uniform disk is mounted with frictionless bearings onto a stationary hor

Question

A solid uniform disk is mounted with frictionless bearings onto a stationary horizontal axle that passes through the center of the disk. The disk has moment of inertia I = 5.0 kg-m2 for rotation about the axle, and radius R = 0.4 m. The disk initially rotates counterclockwise at a rate of 20 rad/s, but at t = 0 a constant clockwise force F = 5 N is applied tangential to the rim of the disk.

a) What is the magnitude of the angular acceleration of the disk?

b) How long does it take the disk to come to rest?

Explanation / Answer

a)

Here , let the magnitude of angular acceleration is a ,

Using second law of motion

I*a = Torque ,

5 * a = 5 * 0.4

a = 0.4 rad/s^2

the magnitude of angular acceleration is 0.4 rad/s^2

b)

Now, using first equation of motion ,

wf = wi + a*t

0 = 20 - 0.4 * t

t = 50 s

the time taken for the disk to come to rest is 50 s

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