physics
posted by aok .
A pulley rotating in the counterclockwise direction is attached to a mass suspended from a string. The mass causes the pulley's angular velocity to decrease with a constant angular acceleration α = 2.2 rad/s2. If the pulley's initial angular velocity is ω = 5.37 rad/s, how long does it take before the angular velocity of the pulley is equal to 3.5 rad/s?

This is a basic rotational kinematics equation.
w= w initial +at
3.5 rad/s = 5.37rad/s + (2.2rad/s2)t
8.87rad/s = (2.2rad/s2) t
t = 4.03 sec