What happens to a cylinder in a closed tube as angular velocity increases?

[giokrutoi]

Homework Statement

the tube is closed at the one end and there is a cylinder
if w increases linearly what will happen to the cylinder
see image attached

Homework Equations

The Attempt at a Solution

I guess that there create vacuum will be created
and this will prevent cylinder from moving but if there is very big ω gained it will fly out at certain w
is that right

 

[Chestermiller]

Homework Statement

the tube is closed at the one end and there is a cylinder
if w increases linearly what will happen to the cylinder
see image attached

Homework Equations

The Attempt at a Solution

I guess that there create vacuum will be created
and this will prevent cylinder from moving but if there is very big ω gained it will fly out at certain w
is that right

What happens in-between?

 

[rude man]

2 parts to this problem:
1. For low w there are two radial forces acting on the core or whatever is inside the cylinder, balancing (not equal in magnitude!) to keep the core fixed in radial position.
2. at some critical w one of these forces disappears, resulting in radial motion of the core.
3. the following is not really a part of your problem but just for your information beyond the critical w there is also a tangential force developed. This force is proportional to w and to radial velocity and is necessary to keep the core rotating..

 

[giokrutoi]

2 parts to this problem:
1. For low w there are two radial forces acting on the core or whatever is inside the cylinder, balancing (not equal in magnitude!) to keep the core fixed in radial position.
2. at some critical w one of these forces disappears, resulting in radial motion of the core.
3. the following is not really a part of your problem but just for your information beyond the critical w there is also a tangential force developed. This force is proportional to w and to radial velocity and is necessary to keep the core rotating..

so you say that it will increase it's displacement from the tube linearly as w increases linearly after some critical w
did I get it right?

 

[giokrutoi]

What happens in-between?

the force by w is so high that vacuum can't hold core inside and the rest space is then replaced by air

 

[rude man]

the force by w is so high that vacuum can't hold core inside and the rest space is then replaced by air

?

 

[rude man]

If you increase w linearly with time you woud have to solve a 2nd order differential equation with a non-constant coefficient which is not solvable by separation of variables. But you can approximate for small dw/dt by assuming w nearly constant, then you get the same equation with constant coefficients & more easily solvable. But in any case the relationship between dx/dt and dw/dt is not linear, it's much more complicated involving hyperbolic sines and cosines. I suggest you not try to make linearity or other quantitative assumptions but just try to see what is happening qualitatively. Realize first of all that there is no force pushing out on the core once critical w is reached. There is always a vacuum on the inside and always atmospheric pressure on the outside.

 

[giokrutoi]

If you increase w linearly with time you woud have to solve a 2nd order differential equation with a non-constant coefficient which is not solvable by separation of variables. But you can approximate for small dw/dt by assuming w nearly constant, then you get the same equation with constant coefficients & more easily solvable. But in any case the relationship between dx/dt and dw/dt is not linear, it's much more complicated involving hyperbolic sines and cosines. I suggest you not try to make linearity or other quantitative assumptions but just try to see what is happening qualitatively. Realize first of all that there is no force pushing out on the core once critical w is reached. There is always a vacuum on the inside and always atmospheric pressure on the outside.

so you assume that it won't come out of tube until critical w

 

[Chestermiller]

so you assume that it won't come out of tube until critical w

Have you drawn a free body diagram showing the forces acting on the mass? If so, please let us see it.

 

[rude man]

so you assume that it won't come out of tube until critical w

Not assume - know!
Yes. w is the one number you should be able to compute and understand.
And do what chestermiller says.

 

[giokrutoi]

so something like the image in attachment
where f =ma = w^2 r

 

[Chestermiller]

so something like the image in attachment
where f =ma = w^2 r

This is not correct. I still don't see a free body diagram and a radial force balance. How can you expect to solve this problem if you don't do this?

Also, are you aware that the acceleration in the radial direction is $\frac{d^2r}{dt^2}-\omega^2 r$?

 

[giokrutoi]

This is not correct. I still don't see a free body diagram and a radial force balance. How can you expect to solve this problem if you don't do this?

Also, are you aware that the acceleration in the radial direction is $\frac{d^2r}{dt^2}-\omega^2 r$?

SORRY but I don't know how to do that

 

[Chestermiller]

Are you saying that you are being taught Physics, but you are not being taught how to draw and use Free Body Diagrams?

 

[giokrutoi]

Are you saying that you are being taught Physics, but you are not being taught how to draw and use Free Body Diagrams?

nope I don't know it I m in high school

 

[Chestermiller]

nope I don't know it I m in high school

Are you trying to learn it on your own, or is this a high school course? Is there a textbook? If so, does the textbook discuss free body diagrams anywhere?

Chet

 

[giokrutoi]

Are you trying to learn it on your own, or is this a high school course? Is there a textbook? If so, does the textbook discuss free body diagrams anywhere?

Chet

nope I saw it in teachers examine test and I am trying to figure it out which answer is correct and how it works.

 

[Chestermiller]

nope I saw it in teachers examine test and I am trying to figure it out which answer is correct and how it works.

Good luck