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 10.0s before coming to rest.
Part A

If its initial angular speed was 3890rpm , what is the magnitude of its angular deceleration? (|?| in revs/s^2 )

Part B

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

Answer 1

Answer:

$a_r=389\ rev.s^{-2}$

$n=58350 rev$

Explanation:

Given:

time of constant deceleration, $t=10\ s$

A.

initial angular speed, $N_i=3890\ rpm$

Using equation of motion:

$N_f=N_i+a_r.t$

$0=3890+a_r\times 10$

$a_r=389\ rev.s^{-2}$

B.

Using eq. of motion for no. of revolutions, we have:

$n=N_i.t+\frac{1}{2} a_r.t^2$

$n=3890\times 10+0.5\times 389\times 100$

$n=58350\ rev$