From the information given, the object starts from rest. This means that
initial angular velocity, wo = 0
It achieves an angular speed of 33,500 rev/min. This means that
final angular velocity, wf = 33,500 rev/min
We would convert 33,500 rev/min to rev/s by dividing by 60. It becomes
558.33 rev/s
time required = 1.6
We would calculate the angular displacement, θ during this period this period by applying the formula,
θ = 1/2(wo + wf)t
θ = 1/2(0 + 558.33)1.6
θ = 446.664 rev
The object continued at this speed for 50s. This means that the angular acceleration is zero since the speed was constant. During this period,
wo = 558.33 rev/s
a = 0
t = 50
We would find the number of revolutions by applying the formula,
θ = wot + 1/2at^2
θ = 558.33 * 50 + 1/2 x 0 x 50^2
θ = 27916.5 rev
Total number of revolutions at this point is
446.664 + 27916.5 = 28363.16 revs
For the final part,
It returns to rest after 10 s. Thus,
t = 10
wf = 0
wo = 558.33
We would find the number of revolutions in this part by applying the formula
θ = 1/2(wo + wf)t
θ = 1/2(558.33 + 0)10
θ = 2791.65 rev
Total revolutions completed is
28363.164 + 2791.65 = 31154.81 revolutions