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A centrifuge in a medical laboratory rotates at a speed of 3290 rev/min. When switched off, it rotates 47.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.
A centrifuge in a medical laboratory rotates at a speed of 3290 rev/min. When switched off, it rotates 47.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.
It’s AVERAGE angular velocity during the slowdown will be 1645 [since it is going from 3290 to 0 uniformly].
It rotates 47 times during the time it slows down, so it must have taken it 47/1645 =1/35 minutes to slow down.
It had to go from 3290 rev/min to 0 in 1/35 minutes, so its deceleration was:
3290*35 = -115150 rev/min^2 = -32.0 rev/s^2 = -201 radians per second squared.
convert the rev/min to radians/minute
3290*2*pi=20672 rad/min
47*2*pi= 295 rad
use wfinal^2=winitial^2+2*alpha*radians
wfinal=0
winitial=20672
radians=295
solve for alpha:
alpha = -20672^2/2/295=-724267radians/min^2 or 115271 rev/min^2