Need help getting started Cylindrical centrifuge

[IntegrateMe]

A cylindrical centrifuge of radius 1m and height 2m is filled with water to a depth of 1m. As the centrifuge accelerates, the water level rises along the wall and drops in the center.

(a) Find an equation of the parabola when the water level rises in terms of h, the depth of water at its lowest point (the lowest point on the parabola).

I don't really know where to go with this. It seems that both sides of the container will be filled with an equal amount of water when the parabola is formed, but I'm just not seeing any connections with how to actually come to an equation.

If anyone has any insight it'd be highly appreciated.

Thanks for the help, everyone!

 

[IntegrateMe]

Should I start by taking the volume of water in the cylinder? Also, will a normal parabola function help me in any way...y = kx^2, for example?

 

[sunjin09]

A cylindrical centrifuge of radius 1m and height 2m is filled with water to a depth of 1m. As the centrifuge accelerates, the water level rises along the wall and drops in the center.

(a) Find an equation of the parabola when the water level rises in terms of h, the depth of water at its lowest point (the lowest point on the parabola).

I don't really know where to go with this. It seems that both sides of the container will be filled with an equal amount of water when the parabola is formed, but I'm just not seeing any connections with how to actually come to an equation.

If anyone has any insight it'd be highly appreciated.

Thanks for the help, everyone!

Basically the sum of gravity and centrifugal force must point perpendicular to the parabola curve everywhere on the parabolar

 

[IntegrateMe]

I appreciate the response, however it doesn't really help me, it only made things more confusing.

 

[sunjin09]

I appreciate the response, however it doesn't really help me, it only made things more confusing.

My apologies, there's no physics in this problem, all you have to do is parametrize your parabola as y=ax^2+h, and calculate the total volume of the water underneath this curve, which must be equal to the total water you start with, from which you solve for a, which will be a function of h.

( Then you can find the angular velocity of the rotation as a function of h, which will involve some physics as I mentioned earlier. )