# What will happen if ω goes up

1. Jul 21, 2017

### giokrutoi

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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

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Last edited by a moderator: Jul 21, 2017
2. Jul 21, 2017

### Staff: Mentor

What happens in-between?

3. Jul 21, 2017

### 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..

4. Jul 22, 2017

### giokrutoi

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?

5. Jul 22, 2017

### giokrutoi

the force by w is so high that vacuum cant hold core inside and the rest space is then replaced by air

6. Jul 22, 2017

### rude man

?

7. Jul 22, 2017

### 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.

8. Jul 22, 2017

### giokrutoi

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

9. Jul 22, 2017

### Staff: Mentor

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

10. Jul 22, 2017

### rude man

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

11. Jul 22, 2017

### giokrutoi

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

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12. Jul 22, 2017

### Staff: Mentor

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 $\frac{d^2r}{dt^2}-\omega^2 r$?

13. Jul 23, 2017

### giokrutoi

SORRY but I don't know how to do that

14. Jul 23, 2017

### Staff: Mentor

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

15. Jul 23, 2017

### giokrutoi

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

16. Jul 23, 2017

### Staff: Mentor

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

Chet

17. Jul 23, 2017

### giokrutoi

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

18. Jul 23, 2017

### Staff: Mentor

Good luck

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