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 11.6 s before coming to rest.

If its initial angular speed was 3523 rpm, what is the magnitude of its angular deceleration? Give answer in rev/s2

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

Explanation / Answer

Given,

t = 11.6 s ; wi = 3523 rpm = 368.93 rad/s

We know from eqn of circular motion

w = wi + alpha t

alpha = (w - wi)/t

alpha = (0 - 368.93)/11.6 = -31.8 rad/s^2

hence, alpha = -31.8 rad/s^2

we know that

theta = wi t + 1/2 alpha t^2

theta = 368.93 x 11.6 - 0.5 x 31.8 x 11.6^2 = 2140.08 rad

N = theta/2 pi = 2140.08/2x3.14 = 340.78 rev

Hence, N = 340.78 rev

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