Question

Life scientists use ultracentrifuges to separate biological components or to remove molecules from suspension. Samples in a symmetric array of containers are spun rapidly about a central axis. The centrifugal acceleration they experience in their moving reference frame acts as "artificial gravity" to effect a rapid separation. If the sample containers are 13 cm from the rotation axis, what rotation frequency is required to produce an acceleration of
1.40 · 105 g?

The answer is supposed to be 517 1/s. How do I arrive at this answer. Thank you very much in advance.

Answer 1

Ac = v^2/r = w^2 r
where w = omega, angular speed = 2 pi f

1.4 *10^5 * 9.8 = w^2 (.13)
w^2 = 106 * 10^5 = 10.6 * 10^6
so
w = 3.25 * 10^3 = 3250 radians/s
f = w/2 pi = 517 sure enough