Uniform Circular Motion of a centrifuge

[Physicsnoob90]

Homework Statement

A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the container. Suppose the centripetal acceleration of the sample is 6.43 x 10^3 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 4.98 cm from the axis of rotation?

Homework Equations

The Attempt at a Solution

1. 6.43x10^3 (9.8 m/s^2) = ω^2 (0.0498 m)

2. ω= 1124.874 rad/s * 1rev/2πrads * 60s/min = 106016.8768 rpm

 

[mfb]

ω= 1124.874 rad/s

That would be correct.

ω= 1124.874 rad/s * 1rev/2πrads * 60s/min

But that is not.
The answer is right again, but you cannot write an equal sign between two things that are not equal.

 

[Physicsnoob90]

But isn't the second step necessary to covert my answer to rpm?

 

[mfb]

The step is necessary, but it is not necessary to make wrong equations. Calculate ω first (ω=...), then use ω in a different equation to calculate rpm.

 

[Physicsnoob90]

got it. Thanks!