Biophysics Problem 43

Assume a man's arm is 0.6 m long and that he can rotate it about his shoulder in a vertical circle once per second. Compare the centripetal force developed with the gravitational frorce on the blood in his hand. (Note that the two forces will be the same ratio as the accelerations.)

Note that:

\(\mathrm{\frac{F_{centripital}}{F_{gravitational}}=\frac{a_{centripital}}{a_{gravitational}} }\)

Remember also that \(\mathrm{a_{centripetal} = r \omega^2}\)
If the arm makes one revolution per second, then \(\mathrm{\omega = 2 \pi \;rad s^{-1}.}\)
What value do you find for the ratio of the forces?

 \(\mathrm{\frac{F_{centripetal}}{F_{gravitational}} = \frac{ (0.6 \;m) (2 \pi \;rad s^-1)^2}{9.8 \;m \;s^{-2}}}\)
And you should find that this ratio gives you \(\mathrm{2.42}\).