# How Do You Calculate Centripetal Acceleration in a Blood Centrifuge?

• Jpyhsics
In summary, a centrifuge is a laboratory device used for spinning samples of material. The equation T=2πr/f cannot be correct as you can tell by doing a unit analysis of the equation.
Jpyhsics

## 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 don't think I did this correctly, as I didnt use the angle...
I have included a photo as well,

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Jpyhsics said:

## 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.

TSny said:
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)?

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

Jpyhsics said:
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.

Jpyhsics said:
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?

TSny said:
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?

Jpyhsics said:
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! :)

Jpyhsics said:
Oh I see how the angle relates now. I got an answer of 10749 m/s2. Thank you so much for your help! :)

## What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle and is caused by a force called the centripetal force.

## What is the formula for calculating centripetal acceleration?

The formula for calculating centripetal acceleration is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

## What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of the circle, while tangential acceleration is the acceleration along the tangent of the circle. In other words, centripetal acceleration changes the direction of the object's velocity, while tangential acceleration changes its magnitude.

## How does centripetal acceleration affect the motion of an object?

Centripetal acceleration causes an object to continuously change its direction, as it moves in a circular path. This means that the object is accelerating, even if its speed remains constant.

## What are some real-life examples of centripetal acceleration?

Some examples of centripetal acceleration in everyday life include the motion of a car around a curved road, the rotation of a Ferris wheel, and the orbit of planets around the sun. Centripetal acceleration is also important in the functioning of centrifuges, carnival rides, and roller coasters.

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