A centrifuge takes 1 minute to turn through 20 complete revolutions before reaching it's final speed. What is the angular acceleration (assumed constant) and what was it's final angular speed in rpm? How do I solve this without knowing the radius of the centrifuge?

Question

A centrifuge takes 1 minute to turn through 20 complete revolutions before reaching it's final speed. What is the angular acceleration (assumed constant) and what was it's final angular speed in rpm?   How do I solve this without knowing the radius of the centrifuge?

drwls · Answer

Let angular acceleration = alpha
(1/2)*(alpha)*t^2 = 20*2 pi
= 40*pi radians

alpha = 80*pi/60^2 = 0.06981 rad/s^2

Final angular speed = alpha*t = 4.19 rad/s
OR
= 2*(average angular speed)
= 2*(40 pi/60)= (4/3)*pi
(same answer)