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 11 rev/s; 65 revolutions later, its angular speed is 17 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 65 revolutions, (c) the time required to reach the 11 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 11 rev/s angular speed.

(a) Number Unit This answer has no unitsdegreesmkgsm/sm/s^2radrad/srad/s^2revrev/srev/s^2NJJ/kgN/kgWN•mkg•m/skg•m^2m^2times (b) Number Unit This answer has no unitsdegreesmkgsm/sm/s^2radrad/srad/s^2revrev/srev/s^2NJJ/kgN/kgWN•mkg•m/skg•m^2m^2times (c) Number Unit

Explanation / Answer

a. Average rotational speed in the interval is (11 + 17) / 2 = 14 revs / s.

At 14 revs / s, it takes 4.643 seconds to rotate 65 times. So the angular acceleration is (17 -11) / 4.643 = 1.29226 rev / s2

b. Time required is , t= 65 rev/14 rev/s=4.643 s

c. (11 rev / s) / (1.292 rev / s2) = 8.51216 seconds

d. 5.5 rev / s * 8.51216 s =46.8169 revs.

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