Physics: Principles with Applications (7th Edition)

The centrifuge must rotate at a rate of $4 \times 10^4 rpm$.
We can find the required acceleration as follows: $a = 125,000\times 9.80 ~m/s^2$ $a = 1.23\times 10^6 ~m/s^2$ We can then use the acceleration to find the velocity: $a = \frac{v^2}{r}$ $v = \sqrt{ar}$ $v = \sqrt{(1.23\times 10^6 ~m/s^2)(0.0700 ~m)}$ $v = 293 ~m/s$ Now, we use the velocity to find the number of revolutions each second: Let z be the number of revolutions each second. $z \times 2\pi r = v$ $z = \frac{v}{2\pi r}$ $z = \frac{293 ~m/s}{(2\pi)(0.0700 ~m)}$ $z = 666 ~rev/s$ The number of revolutions per minute is $60z$; $60z = (60 ~s/min)(666 ~rev/s) = 4 \times 10^4 rpm$ Therefore, the centrifuge must rotate at a rate of $4 \times 10^4 rpm$.