# Centripetal Force Water Parabola

#### Abstract

Water in a spinning tank forms a parabolic surface. Explaining this in terms of centripetal force is non-trivial and very instructive.

Yes

#### Principles Illustrated

It is easy to misleadingly explain this effect in terms of centrifugal force. It is more difficult but better to explain it in terms of centripetal force.

Tertiary

#### Instructions

We show students the demonstration and then ask them to explain the shape in terms of centripetal force. Begin with and imaginary chunk of water and ask what supplies the inward centripetal force. Once students work out that it is the pressure gradient, point out that the centripetal force (at constant angular frequency) is proportional to radius, so the pressure gradient must be proportional to radius. This leads to a parabolic surface in a couple of lines of calculus and algebra.

Then ask how the shape forms in the first place. That generates some discussion.

#### Safety

Our version of the apparatus has relatively little torque due to current limiting. It takes a while to speed up and you can stop it easily. Even then, you want to keep your hands clear.

Individual teachers are responsible for safety in their own classes. Even familiar demonstrations should be practised and safety-checked by individual teachers before they are used in a classroom.

#### Notes

Large parabolic telescope mirrors can be made essentially this way.