Ultracentrifuge Angular Speed Calculation

[richylai]

[SOLVED] Ultracentrifuge Problem

Find the required angular speed (in rpm) of an ultracentrifuge for the radial acceleration of a point .0250 m from the axis to equal 400000g. g=9.8 m/s^2.

 

[richylai]

Oh sorry I put this in the wrong subforum.

 

[berkeman]

Looks like it got moved okay. You need to show us your work in order for us to offer tutorial help (that's the rules). What is the equation that relates angular velocity to angular acceleration? How would you use that equation (being careful with your units) to solve the problem?

 

[richylai]

I'm not sure but do I have to use Ac = V^2 / R ? Then, after solving for velocity, I would have to convert it to omega? w = V/R ?

 

[berkeman]

I'm not sure but do I have to use Ac = V^2 / R ? Then, after solving for velocity, I would have to convert it to omega? w = V/R ?

That sounds like a good approach.

 

[Hootenanny]

I'm not sure but do I have to use Ac = V^2 / R ? Then, after solving for velocity, I would have to convert it to omega? w = V/R ?

Your on the right track, but the question wants the angular speed in revolutions per minute not radians per second.

Edit: Sorry berkeman, didn't see you there.

 

[richylai]

Oh yea I was aware I had to do unit conversion, but thanks for bringing that up, and thank you for your help Hoot and berk.

 

[richylai]

It seems like the approach is not working. So I first used Ac = V^2 / R and so first I did 400000 * 9.8 * .025 and square rooted the answer to get my Velocity then I divided it by .025 to get my omega which should be in rad/s right now, then I divided it by 2pi and divided it by 60 so that my answer should be in rpm and ended up with 33.2 rpm, which the system says is wrong.

 

[berkeman]

It seems like the approach is not working. So I first used Ac = V^2 / R and so first I did 400000 * 9.8 * .025 and square rooted the answer to get my Velocity then I divided it by .025 to get my omega which should be in rad/s right now, then I divided it by 2pi and divided it by 60 so that my answer should be in rpm and ended up with 33.2 rpm, which the system says is wrong.

If you have an answer in revolutions per second, should you divide or multiply to get an answer in RPM?

BTW, it would be best if you carried units along with your calculations for each quantity, and make sure that units are cancelling out with each operation. At each step in manipulating equations, the units on the left side of the + sign must match the units on the RHS. And each additive quantity on the LHS and RHS must have the same units.

Carrying units along with the quantities makes it easy to know whether to divide or multiply by 60. Quiz Question -- why?

 

[richylai]

Ah... dumb me... should've multiplied not divided by 60 -.-' Thank you again...

 

[berkeman]

Ah... dumb me... should've multiplied not divided by 60 -.-' Thank you again...

Good job. Get in the habit of carrying units along in your equations, and you will be amazed at how much that helps you keep things straight. One of the best tricks I learned in my first year of Undergrad.