Question

a fly wheel rotating at constant rate of 120 rpm slows down at constant rate of 2 radian per second how many rotations it take in process

Answer 1

 ω₀ = 120 rpm = 2 rps = 4π rad /sec

    2 rad/sec^2 angular deceleration.
     α = - 2 rad/sec²
     ω = 0 = ω₀ + α t      =>  t = 4 π / 2 = 2 π sec.
 
θ  = ω₀ t + 1/2 * α  t²
   =  4 π * 2 π - 1/2 * 2 * (2π)²   = 4 π²  rad
 Number of rotations = θ/2π = 2 π