A disk rotates about its central axis starting from rest and accelerates with co

Question

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 12 rev/s. 75 revolutions later, its angular speed is 20 rev/s.

(a) Calculate the angular acceleration.
rev/s2

(b) Calculate the time required to complete the 75 revolutions mentioned.
s

(c) Calculate the time required to attain the 12 rev/s angular speed.
s

(d) Calculate the number of revolutions from rest until the time the disk attained the 12 rev/s angular speed.
rev

Explanation / Answer

The problem can be solved as follows:

(a) Average rotational speed in the interval is (12 + 20) / 2 = 16 revs / s.

At 16 revs / s, it takes 4.687 seconds to rotate 75 times.

So the angular acceleration is (20 - 12) / 4.687 = 1.707 rev / s^2

(b) As calculated above, it is 4.687 sec.

(c) (12 rev / s) / (1.707 rev / s^2) = 7.03 seconds

(d) 12 rev / s * 7.03 s = 84.36 revs.

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