# Paraboloid of revolution

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(Parabaloid of revolution)

Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.

Hint: consider a particle of liquid located at (x, y) on the surface of the liquid.

The forces acting on the particle are m*W^2*x in the x direction and -m*g in the y direction.

As the particle is in radial and equilibrium the resultant vestor is normal to the curve.

Please solve by writing and solving the appropriate 1st order equation and show how the curve containing the particle is found.

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##### Solution Summary

The problem is solved by considering various forces acting on a particle of liquid on the surface and the conditions for its equilibrium.

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Please refer attachment for solution.

Solution

Y

ω

P(x,y)

F1

θ θ

Liquid surface A B C

F2 R

X

Let us consider a particle of liquid at point P(x,y) on the surface of the liquid. It will be ...

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