A centrifuge is a common laboratory instrument that separates components of diff

Question

A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 25.4 s before coming to rest.

If its initial angular speed was 3430 rpm, what is the magnitude of its angular deceleration?

How many revolutions did the centrifuge complete after being turned off?

Explanation / Answer

initial angular speed = wi = 3430 rpm = 3430*2*pi/60 = 359.18 rad/s

fianl angular speed = wf = 0

time taken to come to rest = t = 25.4 s

angular acceleration alfa = (wf-wi)/t

alfa = (0-359.18)/25.4 = -14.14 rad/s^2

magnitude = 14.14 rad/s^2

------------

theta = wi*t + 0.5*alfa*t^2

theta = (359.18*25.4) - (0.5*14.14*25.4^2)

theta = 4562 rad = 4562*(1/(2*pi)) = 726.06 revolutions    <<----answer

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