# Centripetal Acceleration

## Homework Statement

A centrifuge is a laboratory device used for spinning samples of material. In a blood centrifuge, a test tube is inserted at an angle θ=32.0° with respect to the vertical and the whole sample is spun at high speed. For a typical test that is l= 15.9 cm long and is spun in a centrifuge at a rate of 4316 rotations per minute, what is the centripetal acceleration experienced by the sample at a point x=9.93 cm from the rotation axis, as measured along the test tube? Express your answer in units of the standard gravity g. Thus, if your answer is 19.62 m/s2 = 2.00×9.81 m/s2, you would enter 2.00 into the box.

a=v2/r
T=2πr/f
v=d/t

## The Attempt at a Solution

First, I found the period
T=2π(15.9)/(4316/60)=1.3888
v=2π(9.93)/1.3888=71.9
a=(71.9)2/9.93

I dont think I did this correctly, as I didnt use the angle....
I have included a photo as well,

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TSny
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## Homework Equations

a=v2/r
T=2πr/f
v=d/t
The equation T=2πr/f cannot be correct as you can tell by doing a unit analysis of the equation.

3. The Attempt at a Solution
First, I found the period
T=2π(15.9)/(4316/60)=1.3888
v=2π(9.93)/1.3888=71.9
a=(71.9)2/9.93
You need to be clear on the meaning of r in the equations. You want the centripetal acceleration of a particular point in the test tube. Mark this point in your diagram and try to draw a representation of r in the diagram.

The equation T=2πr/f cannot be correct as you can tell by doing a unit analysis of the equation.

You need to be clear on the meaning of r in the equations. You want the centripetal acceleration of a particular point in the test tube. Mark this point in your diagram and try to draw a representation of r in the diagram.
So how what formulas would I have to use?
I would assume ac=v2/r? but what about the period (T)?

So how what formulas would I have to use?
Would I use the 15.9cm?

TSny
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Gold Member
So how what formulas would I have to use?
You should be able to solve it using your two equations

a=v2/r
v=d/t

But if you have learned how to write centripetal acceleration in terms of angular velocity ω, you might find that to be a quicker way to the answer.

TSny
Homework Helper
Gold Member
but what about the period (T)?
If the test tube makes 4316 revolutions in one minute, how much time does it take for it to make one revolution?

If the test tube makes 4316 revolutions in one minute, how much time does it take for it to make one revolution?
0.0139s per rotation?

0.0139s per rotation?
Oh I see how the angle relates now. I got an answer of 10749 m/s2. Thank you so much for your help! :)

TSny
Homework Helper
Gold Member
Oh I see how the angle relates now. I got an answer of 10749 m/s2. Thank you so much for your help! :)