Answer
The centrifuge must rotate at a rate of $4 \times 10^4 rpm$.
Work Step by Step
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 $4 \times 10^4 rpm$.
