# Biophysics Problem 42

A lab technician is centrifuging a blood sample at an angular speed of $3000\; rpm$ (revolutions per minute). If the radius of the circular path followed by the sample is $0.15 \;m,$ find the speed of the sample in $m/s.$

#### First Step

Recall that the speed of a rotating object is $v = \omega r.$  Also, it is necessary to realized that \omega is the angular speed in  $\text {radians per second} \;(rad s^{-1}).$

Since r is known $(r = 0.15 \;m),$ all we need to do is find and substitute \omega into the above speed equation.

$\omega = 2 \pi f$

Calculate $\omega.$

#### Calculations

The frequency $f$ must be measured in Hertz (cycles per second). So,

$f = 3000 \;RPM = \frac{3000 \;\text{revolutions}}{60 \;\text{seconds}} = 50 s^{-1}.$

For angular speed, you should have had

$\omega = 2 \pi f = 2 \pi \;(50 x^{-1}) = 314 \;rad s^{-1}$

Then, substituteing r and \omega into the equation $v = r \omega,$ you should get

$v = 47.1 m\; s^{-1}$