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 10.0 rev/s. After 60 more complete revolutions, its angular speed is 11.756 rev/s.. Calculate the angular acceleration.

Calculate the time required to complete the 60 revolutions mentioned.

Calculate the time required to attain the 10.0rev/s angular speed.

Calculate the number of revolutions from rest until the time the disk attained the 10 rev/s. angular speed.(no unit)

Explanation / Answer

a.      Average rotational speed in the interval is

       (10 + 11.756) / 2 = 10.878 rev / s.

       At 10.878 revs / s, it takes = 60/10.878 = 5.5157 seconds to complete the 60 revolutions .

     So the angular acceleration is (11.756 - 10) / 5.5157 =        0.3183 rev / s^2

b. it takes = 60/10.878 = 5.5157 seconds to complete the 60 revolutions .

c. (10 rev / s) / (0.3183 rev / s^2) = 31.41 seconds

d. 10 rev / s * 31.41 s = 314.1 revs.

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