Question

After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 6.40 rad/s and it rotated 14.3 revolutions before coming to rest.

Answer 1

a)Initial angular velocity w0 = 6.40 rad/s
Angular displacement theta = 14.3 rev = 14.3 * 2 pi rad = 89.84 rad
Final angular velocity w = 0

Let angular acceleration = alpha
w^2 = w0^2 + 2 * alpha * theta
0 = 6.40^2 + 2 * alpha * 89.84
0 = 40.96 + 179.68 * alpha
alpha = - 40.96/179.84 = - 0.227 rad/s^2
Ans: - 0.227 rad/s^2

b) Let time = t
w = w0 + alpha * t
Or 0 = 6.40 - 0.227 * t
Or t = 6.40/0.227 = 28.193 s