# Centrifugal force on water in a glass

1. Jan 28, 2017

### srecko97

1. The problem statement, all variables and given/known data
There is a cyllindrical glass (r=0.05 m) full of water. It is rotating around its vertical geometric axis with 3 turns per second. How many centimetres higher is water at the rim than in the centre of the glass . Water rotates together with the glass.

2. Relevant equations
p=ρah
ω=2πγ
a=ω2r
3. The attempt at a solution
All I know is that the shape of water is parabolic. In the centre there is no additional pressure from rotation, the pressure on the glass is p=ρah, a=ω2r
total pressure on any point is px + py (vectorial sumation)

2. Jan 28, 2017

### billy_joule

That's right. If we let the vertex be at (0,0) then you just need to find the Y value when X=0.05m.
Start by drawing a free body diagram for a piece of water on the surface.

3. Jan 28, 2017

### srecko97

probably is y=Cx2 ... but I do not know what is C, maybe a/g ... a=17.8 m/s^2, g=10 m/s^2 i do not know, honestly just guessing, as i do not know how to solve it

4. Jan 28, 2017

### billy_joule

Post your FBD and we'll see where you've gone wrong.

5. Jan 29, 2017

### srecko97

I do not know what free body diagram is. Sorry. Please explain to me and I will try

6. Jan 29, 2017

### haruspex

Consider a small parcel of water at the surface, at some radius x. If the surface shape is described by y=f(x), what is the slope there? Draw a diagram of the parcel of water and the forces acting on it. Treat the rest of the water as a frictionless solid.

7. Jan 29, 2017

### srecko97

8. Jan 29, 2017

### haruspex

Ok. You left out a normal force, and you need to answer this question
I.e., in terms of x and y.

9. Jan 29, 2017

### srecko97

tanφ =ω2r / g

10. Jan 29, 2017

### srecko97

and dy/dx = ω2r / g
so: y= ω2r x /g ... for r=x I get y= ω2x2 /2g

11. Jan 29, 2017

### srecko97

and I have y if i put r=x!

12. Jan 29, 2017

### haruspex

Right. So what answer do you get?

13. Jan 29, 2017

### srecko97

4,4cm

14. Jan 29, 2017

### haruspex

Using g=10m/s2, yes, but 4,5cm would be a bit closer.
Well done.