Calculating Angular Displacement in a Centrifuge Rotor

[pb23me]

Homework Statement

A centrifuge rotor is acceleratedfrom rest to 20,000 rpm in 5min.
Through how many turns has the centrifuge rotor turned during its acceleration period?Assume constant angular acceleration.

Homework Equations

The Attempt at a Solution

I just concluded that it made 4,000 rev the first min then 8,000 the second min 12,000 third min 16,000 fourth and 20,000 the 5th. I then added them all to get 60,000 rev... even if this is correct is there a different way of obtaing this answer?

 

[Delphi51]

I don't think your method is correct, though it has considerable ingenuity about it. Because of the constant angular acceleration, it likely reached a speed of 4000 RPM at the END of the first minute. But that would not be 4000 turns during the first minute.

The purpose of this sort of question is to familiarize yourself with the use of the rotational motion formulas so you can solve these problems very quickly and surely. And go on to greater things. I suggest you find the formulas for constant rotational acceleration, study them and try to find one or two that can be applied to this problem. You many need to convert the RPM into the standard unit of rotational velocity, radians per second.

 

[pb23me]

Ok well i have four equations listed in my lab book that i don't know what they are... i listed these four equations on a thread labeled Rotational motion equations. I would like to know what those equations are however no one has responded to me yet. Maybe you could take a look and tell me what those equations are...

 

[pb23me]

ok i did \theta₂=1/2\alpha(t)²
so \theta=314100 rad so dividing that by2\pi i got 49990.5 turns

 

[Delphi51]

Looks good!
By guess and by golly, the average speed would be half of 20,000 RPM or 10,000 RPM. For 5 minutes, 50,000 RPM.
Your answer should be rounded to 4 digit accuracy because you have so rounded pi; ending up with 50 000 RPM both ways.