Outward pressure in rotational motion...

[MDJH]

I mentioned before about centripetal forces, and the idea that if some closed container were spun about a central point such that one end of the container always pointed to said central point, the pressure would be higher at the end further from the centre than away from it.

 

Now that I've gotten to the part relating to rotational motion I was also supposed to have learned in introductory physics, one equation caught my attention; a = r*(w^2). This means that the centripetal acceleration (which for constant mass is proportional to force) is proportional to radius; a bit strange, when you consider a = (v^2)/r, where r is in the denominator; but then you consider that v=rw, ergo v^2 = (r^2)*(w^2) and it makes a bit more sense.

 

However, this also means that within the same rotating object, centripetal force is a function of distance from the rotation axis; even if the axis passes through the object. This also means that the closer you get to the radius, the closer the centripetal force gets to zero. So basically, unless an inner object within it has a centre of mass lying EXACTLY on the axis, centripetal forces will pull it outward, and they will only get stronger and stronger as it goes further out... that is, so long as it's within the rotating object.

 

So, let's say this container was filled with a fluid, whether liquid like water or gaseous like air, and was spun such that its axis of rotation passed right through it. Wouldn't that mean the implicit pressure gradient from the axis of rotation outward would suck fluid away from the middle and bunch it up at the outer sides?

[swansont]

 

However, this also means that within the same rotating object, centripetal force is a function of distance from the rotation axis; even if the axis passes through the object. This also means that the closer you get to the radius, the closer the centripetal force gets to zero. So basically, unless an inner object within it has a centre of mass lying EXACTLY on the axis, centripetal forces will pull it outward, and they will only get stronger and stronger as it goes further out... that is, so long as it's within the rotating object.

 

The centripetal force is directed toward the center, so it is impossible for it to pull anything outward. But that's OK, because forces don't cause motion, they cause acceleration; the mass still moves out. What is actually happening is that the mass "wants" to go along a straight line, in accordance with Newton's laws. If whatever force is present is insufficient to make it move in a circle, then its motion will have a component away from the center. That's why it will move to a larger radius.

 

So, let's say this container was filled with a fluid, whether liquid like water or gaseous like air, and was spun such that its axis of rotation passed right through it. Wouldn't that mean the implicit pressure gradient from the axis of rotation outward would suck fluid away from the middle and bunch it up at the outer sides?

 

Yes. It's called a centrifuge.

[MDJH]

Yes. It's called a centrifuge.

I thought centrifuges were when the whole container revolved around an external axis, rather than rotating about one that passed through the container...

[insane_alien]

I thought centrifuges were when the whole container revolved around an external axis, rather than rotating about one that passed through the container...

 

some are, some aren't. most notably, gas centrifuges.