Question

A roulette wheel with a 1.0m radius reaches a maximum angular speed of 18 rad/s before it stops 35 revolutions ( 220 rad ) after attaining the maximum speed. How long did it take the wheel to stop?
Unless you mean the 35 revs occur after max speed, it cannot be solved.
The average speed on slowing was 18/2 rad/s displacement= avg speed * time solve for time.

Answer 1

Max ang. speed(u) = 18 rad/s
final ang. speed(v) = 0
ang. displacement(s) = 220 rad

ang. acceleration = (v^2 - u^2)/2s = -18^2 / 2*220 = -0.7364 rad/s^2

v = u +at
0 = 18 - 0.7364t
t = 18/0.7364
t = 24.44 seconds