After fixing a flat tire on a bicycle you give the wheel a spin. (a) if its initial angular speed was 6.35 rad/s and it rotated 14.2 revolutions before coming to a rest, what was its average angular acceleration? (b) for what length of time did the wheel rotate?

Part (a)

ω₀ = 6.35 rad/s, initial angular speed

θ = 14.2 rev = 14.2*2π rad = 89.22 rad, angular distance traveled.

Let α = the angular acceleration.

Because the wheel comes to rest,

ω₀² + 2αθ = 0

(6.35 rad/s) ² + 2 * (α rad/s²) * (89.22 rad) = 0

40.3225 + 178.44α = 0

α = - 0.226 rad/s²

Answer: - 0.226 rad/s²

Part (b)

Let t = the time for the wheel to come to rest.

Then

ω₀ + αt = 0

6.35 - 0.226t = 0

t = 6.35/0.226 = 28.1 s

Answer: 28.1 s