A wind turbine rotates at 15.1 rpm and has an angular acceleration of 0.0659 rad/s2. If the wind turbine takes 24.0 s to come to a complete stop, how many revolutions will this take?

Answer 1

THREE WAYS: A, B, and C
omega at start = 15.1 revs/min * 2 pi rad/rev * 1 min/60 s
= 1.58 rad/s
if acceleration is constant then omega is linear and
average omega = 1.58/2 rad/s
1.58/2 * 24 = 19 radians
so
A) 19 radians * 1 rev/6.28 radians = 3.02 revs to stop
or just
15.1 / 2 = 7.55 rpm average = 7.55/60 revs/second
so
B )7.55/60 * 24 = 3.02 revs to stop
Of course you could do it a harder way
angle = omega initial* t - (angular accelertion/2) t^2
= 1.58 * 24 - (0.0659/2)24^2
= 38 - 19 = 19 radians
so
C) 19 /6.28 = 3.02 revs