assume,you are on a big wheel at fair ground vehicles 1 rev every 8 sec,the operator of the wheel decided to stop the wheel by applying brakes.the brake produce on acceleration of 0.1 rad/sec2.your seat is 4m from the axis of rotation
a,what is your velocity before the brakes are applied?
b,How long does it take the big wheel to stop?
c,How many revolution does in the wheel make is slowing down.
angular velocity = 2 pi radians / 8 seconds = 0.785 rad/s approximately
your linear speed = omega R = 0.785 * 4 = 3.14 meters/second
omega = 0.785 rad/s - 0.1 rad/s^2 *t
0 = 0.785 rad/s - 0.1 rad/s^2 *t
t = 7.85 seconds to stop
angle = initial omega t -(1/2)(.1) t^2
or more easily
use average omega for time t
average omega = 0.785 rad/s / 2
so total radians = 0.785 /2 * 7.85 = 3.08 radians
divide by 2 pi to get revolutions, about half a turn