Question

Beckman Instruments sells ultra-centrifuges to separate out (usually suspended organic) materials by density; one of their high-performance models claims a rotational speed of 150,000 rpm which results in over one million gravities of acceleration within the sample tube. Sketch a centrifuge rotor (spoked wheel) and answer the following:

What is the angular velocity omega in radians / second of a centrifuge rotor spinning at 150,000 rpm? Note 1 revolution = 360° = 2π radians.

Answer 1

The angular velocity ω in radians per second of a centrifuge rotor spinning at 150,000 rpm is approximately 15,707.96 radians/s. This is calculated by first converting rpm to revolutions per second (rps) and then converting rps to radians/s using the relation 1 revolution equals 2π radians.

Step-by-step explanation:

To find the angular velocity (ω) in radians per second for a centrifuge rotor spinning at 150,000 revolutions per minute (rpm), we can use the conversion factor where 1 revolution equals 2π radians. First, we convert the speed from rpm to revolutions per second (rps) by dividing by 60, since there are 60 seconds in a minute. After that, we multiply by 2π to convert revolutions to radians.

So, the calculation process is as follows:

• Convert rpm to rps: 150,000 rpm ÷ 60 = 2500 rps
• Convert rps to radians/s: 2500 rps × 2π radians/revolution = 15,707.96 radians/s

The angular velocity of the centrifuge rotor is therefore approximately 15,707.96 radians per second.