How fast (in rpm) must a centrifuge rotate if a particle 9.0 cm from the axis of rotation is to experience an acceleration of 120000 g's?

Sure, let's solve this step by step.

First, we need to understand that the acceleration a particle experiences in a centrifuge is given by the formula:

a = ω²r

where:

• a is the acceleration,
• ω is the angular velocity (in rad/s), and
• r is the distance from the axis of rotation.

We are given:

• a = 120000 g's = 120000 * 9.8 m/s² (since 1g = 9.8 m/s²), and
• r = 9.0 cm = 0.09 m (since 1 cm = 0.01 m).

We can rearrange the formula to solve for ω:

ω = sqrt(a/r)

Substituting the given values:

ω = sqrt((120000 * 9.8) / 0.09)

Calculate the above expression to get the value of ω.

Finally, we need to convert ω from rad/s to rpm (revolutions per minute). The conversion factor is 60/(2π) since there are 2π radians in one revolution and 60 seconds in one minute.

So, the final rpm = ω * 60/(2π)

Calculate the above expression to get the final answer.