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 rev/s. 75 revolutions later, its angular speed is 24 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 10 rev/s angular speed.
___ s

(d) Calculate the number of revolutions from rest until the time the disk attained the 10 rev/s angular speed.
___rev

Explanation / Answer

a. Average rotational speed in the interval is (10 + 24) / 2 = 17 revs / s. At 17 revs / s, it takes 3.529 seconds to rotate 75 times. So the angular acceleration is (24 - 10) / 3.529 = 3.967 rev / s^2

b. Done above.

c. (10 rev / s) / (3.967 rev / s^2) = 2.52 seconds

d. 3 rev / s * 2.52 s = 7.56 revs

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