Question

After fixing a flat tire on a bicycle you give the wheel a spin.
(a) If its initial angular speed was 5.41 rad/s and it rotated 13.7 revolutions before coming to rest, what was its average angular acceleration?

Answer 1

wf^2=wi^2+2*alpha*displacement

where displacement = 13.7*2PI radians
wi=5.41 rad/sec, wf=0
solve for angular acceleration, in rad/s^2

Answer 2

13.7 * 2 pi = 86.08 radians total

average speed = 2.705 rad/s
so time to stop = 86.08/2.705 = 32.8 seconds

d = Vi t +(1/2) a t^2

86.08 = 5.41 (32.8) +.5 a (32.8)^2

86.08 = 172 + 538 a

-86 = 538 a

a = - 0.16 rad/s^2