How fast (in rpm) must a centrifuge rotate if a particle 6.00 cm from the axis of rotation is to experience an acceleration of 125,000 g's?

A particle at 6 cm from the axis of rotation has radius

r = 6 cm = 0.06 m

The expected acceleration is

a = 125,000 g's = 125000 * (9.8 m/s²) = 1.225 x 10⁶ m/s²

Let ω = the angular velocity.

The acceleration is centripetal, and it is given by

a = ω²r

Therefore

(ω rad/s) ² * (0.06 m) = 1.225 x 10⁶ m/s²

ω² = 2.0417 x 10⁷

ω = 4518.5 rad/s

= (4518.5 rad/s) * (1/2π rev/rad)

= 719.14 rev/s

ω = (719.14 rev/s) * (60 s/min)

= 43148.5 rpm

Answer: 43149 rpm (nearest integer)