how many revolutions did it turn in this time.?

Question

A centrifuge accelerates uniformly from rest to 15,000rpm in 220s. through how many revolutions did it turn in this time.

This ? is about constant angular acceleration; rolling

thanx for your help.

Answer 1

θ = θ0 + ω0t + (1/2)αt^2
For uniform acceleration, α = ω/t
α = (15,000 rpm)(1 min/60 s)/(220 s)
α = (25 rev)/(22 s^2)
θ = 0 + 0 + (1/2)((25 rev)/(22 s^2))(220 s)^2
θ = 27,500 revolutions

Answer 2

15000rpm = 250rps. Uniform acceleration means that the average rps was 125, so in 220s, it revolved 125*220 = 27500times.