The Shape of the Surface of a Rotation Liquid (UMAP)

A unit that applies calculus to engineering and physics. By completion of this module students will be able to analyze the forces on a liquid rotating in a vertical cylinder at constant angular speed to show that the surface of the liquid is a paraboloid of revolution.

Table of Contents:

1. THE BASIC PROBLEM

2. THE MATHEMATICAL MODEL
2.1 The Simplifying Assumptions
2.2 Computing the Forces
2.3 The Centripetal Force
2.4 The Surface is Identified

3. SOME ADDITIONAL COMMENTS
3.1 Parabolic Mirrors
3.2 Planar Motions of a Mars Particle

4. REFERENCES

5. EXERCISES

6. ANSWERS TO EXERCISES