Centripetal Acceleration Problem

[Kieran12]

Homework Statement

A centrifuge rotates at 12000rpm, what is the radians per second? If the radius of the centrifuge is 150mm, what is the centripetal acceleration?

Homework Equations

Angular Velocity: ω = Δθ/Δt (maybe, not sure)

Centripetal Acceleration: a = v² / r

The Attempt at a Solution

To get the radians per second, I did 12000 x 2π = 24000π rads/min. Then to get this in rads/sec I just did 24000π / 60 = 400π rads/sec
This gives me the tangential velocity (I think).

Then for to get the centripetal acceleration, I firstly converted the 400π rads/sec to metres/sec: 400π x 0.150 = 60π = 188.5 m/s.

I then used the formula for Centripetal Acceleration to get: a = 188.5² / 0.150
Which gave me: a = 236881.6 m/s²
Any and all help is welcome! If I've done this completely wrong please feel free to destroy everything I thought true and correct me like a Physics martyr.

 

[BvU]

Hello Kieran and welcome to PF. I am also a newbie and I wonder if PF is meant to help all to score A++ or whatever regional markings exist.

On the other hand, your posting is exemplary. Completely clear.

You have done the exercise, checked the results. Is there something you are uncomfortable with, or something you would like to have explained ?

The 'not sure' part: yes, radians per second is radians divided by seconds. Same as with meters per second for speed. Normally a differential, but for uniform rotation a ratio.

And, to cap: I can't find anything wrong in what you did. Does that help ?

 

[Kieran12]

Erm. I'd like someone to explain what I've done wrong, where I've gone wrong and what I need to do to make it un-wrong.

 

[PhanthomJay]

Looks good! Note that you don't have to convert to tangential speed you can directly use centripetal acc = w^2(r).

 

[NascentOxygen]

Hi Kieran12! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

All looks correct.