Purchase Solution

# Paraboloid of revolution

Not what you're looking for?

(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.

##### 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.

##### Solution Preview

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 ...

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.