# 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 \(m/s.\)

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 \(\omega.\)

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

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