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## Homework Statement

"A bucket of water is set spinning around its symmetry axis, determine the shape of the water in the bucket"

## Homework Equations

**F=-**m

**ω×(ω×r)**(centrifugal force)

## The Attempt at a Solution

I first found the centrifugal force on a small mass of water (

**F**=mω²

**r**), then I integrated this with respect to r to find the potential energy associated with the centrifugal force [U=-(mω²/2)r²]. Since the water is bound in the bucket, it cannot attain any kinetic energy, thus in equilibrium the potential energy due to the centrifugal force must cancel the gravitational potential energy U=mgz. Solving for z, I got z=(ω²/2g)r², thus the water forms a paraboloid.

Is my reasoning correct? Thank you in advance.