# Centripetal Force & Gas Centrifuges

• Jimmy87
In summary: for a gas centrifuge, but the exact value may vary depending on the specific design and operating conditions.
Jimmy87
Hi,

I am studying circular motion at the moment and we were asked to go away and find an example of a device which has a very large centripetal acceleration. Initially I found a washing machine has up to about 300g but then I was looking at nuclear enrichment gas centrifuges which have huge accelerations. I can;t find a source that mentions the acceleration but I have found sources that tell you the information you need:

Radius of Centrifuge = 4 inches
Frequency of Rotation = 2000Hz

a = v2/r

v = 2πf

So, a = (2πf)2/r = (2π x 2000)2/0.1016 = 1.55 x 109 ms-2

So I come to my main question - what have I done wrong as this is way too high.

I also have a second question. When an object is undergoing uniform circular motion how do you interpret the acceleration. What I mean is that it is really easy to understand a car accelerating in a straight line because it tells you how many m/s his speed is increasing every second. For example, an acceleration for a car of 3m/s2 that is not changing direction means that every second the speed is increasing by 3m/s. What does 3m/s2 mean when the object is going round in a circular at constant speed though. How can 3m/s every second relate to a change in direction?

Thanks for any help,

Jimmy87 said:
v = 2πf
This is obviously false as the units do not match. The left-hand side has units of length/time and the right-hand side has units of 1/time.
Jimmy87 said:
What does 3m/s2 mean when the object is going round in a circular at constant speed though. How can 3m/s every second relate to a change in direction?
Acceleration is not the change in speed, which is a scalar. It is the change in velocity, which is a vector.

Jimmy87
Orodruin said:
This is obviously false as the units do not match. The left-hand side has units of length/time and the right-hand side has units of 1/time.

Acceleration is not the change in speed, which is a scalar. It is the change in velocity, which is a vector.

Thanks - how silly of me. So would it be:

So, a = (2πfr)2/r = (2π x 2000 x 0.1016)2/0.1016 = 1.6 x 107 ms-2

That still seems very high - is that plausible for a gas centrifuge?

About my second question - I think I wasn't clear with what I was asking. I know velocity is a vector and that the speed can remain constant whilst the object is accelerating (e.g. circular motion). However, how do you interpret the value of the acceleration if the speed is remaining constant? If the acceleration is 3m/s2 for example and the speed is not changing then what does 3m/s per second actually mean? That the direction is changing by 3m/s per second? What does that even mean?

I am sorry, but I cannot understand how you can say this
Jimmy87 said:
I know velocity is a vector and that the speed can remain constant whilst the object is accelerating (e.g. circular motion).
and yet not be ok with this
Jimmy87 said:
However, how do you interpret the value of the acceleration if the speed is remaining constant?
Acceleration is change of velocity with time, if there is a non-zero acceleration, then the velocity will be different at a later time. If the difference in time is small, then
$$\vec v_2 = \vec v_1 + \vec a (t_2-t_1).$$
All that is being said is how the velocity changes with time for small times. Note that acceleration is also a vector, it has a direction - the direction in which the velocity changes.

Jimmy87
A.T. said:

Thanks. The second answer with the diagram is what I was looking for - thank you.

Orodruin said:
I am sorry, but I cannot understand how you can say this

and yet not be ok with this

Acceleration is change of velocity with time, if there is a non-zero acceleration, then the velocity will be different at a later time. If the difference in time is small, then
$$\vec v_2 = \vec v_1 + \vec a (t_2-t_1).$$
All that is being said is how the velocity changes with time for small times. Note that acceleration is also a vector, it has a direction - the direction in which the velocity changes.

I am perfectly fine with the fact that an object can accelerate even though speed is constant. Changing direction requires a resultant force and F=ma tells us there must then be an acceleration. It is not this I am not ok with it is just interpreting the value of the acceleration in terms of changing direction only. It makes perfect sense to say that an acceleration of 3m/s2 means that the speed increases by 3m/s every second. However, if the speed is constant then we are now saying that the direction changes by 3m/s every second. I can see it mathematically but can't picture what that means. Would that equation you gave work for acceleration at constant speed? The magnitude of your v2 will be different to v1 and I thought the magnitude is the speed and won't change in this example?

Jimmy87 said:
The magnitude of your ##v_2## will be different to ##v_1##
In uniform circular motion, the magnitude of ##v_2## and ##v_1## will be identical. But, because their directions are different, their vector difference will be non-zero. If the difference in angle between ##v_1## and ##v_2## is tiny, the vector difference can be visualized as the base of a tall, thin isoceles triangle with ##v_1## and ##v_2## as the equal sides and the vector difference as the remaining side.

Jimmy87

## 1. What is centripetal force?

Centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. This force is necessary to keep the object moving in a circular motion instead of flying off in a straight line.

## 2. How does centripetal force apply to gas centrifuges?

In gas centrifuges, centripetal force is used to separate different types of gas molecules based on their mass. The heavier molecules are forced towards the outer edge of the centrifuge, while the lighter molecules remain closer to the center.

## 3. What is the purpose of using gas centrifuges?

Gas centrifuges are used to enrich uranium for nuclear fuel or weapons. The centrifuge separates the heavier uranium-238 isotope from the lighter uranium-235 isotope, increasing the concentration of uranium-235 for use in nuclear reactions.

## 4. How is the speed of a gas centrifuge determined?

The speed of a gas centrifuge is determined by the strength of the centripetal force applied and the mass of the object being centrifuged. The higher the speed, the greater the centripetal force and the stronger the separation of the gas molecules.

## 5. Are gas centrifuges safe to use?

Gas centrifuges can be dangerous if not properly maintained or if there is a malfunction. The centrifuges must be carefully monitored and controlled to prevent accidents. However, when used correctly, gas centrifuges are a safe and effective method for enriching uranium.

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