Thread: What is a Cyclonical curve?

1. What is a Cyclonical curve?

Hi everyone,

Recently in a problem I encountered the word cyclonical curve. Do you have any idea what this is? One of the ideas that I thought of is a cyclone can be approximated to a spiral. But then there are many different kind of spirals.......

2. Originally Posted by Sudharaka
Hi everyone,

Recently in a problem I encountered the word cyclonical curve. Do you have any idea what this is? One of the ideas that I thought of is a cyclone can be approximated to a spiral. But then there are many different kind of spirals.......

Cyclonical - pertaining to a cyclone, so in this case a curve that spirals (inward if direction has a sense)

Is there more context available?

CB

3. Originally Posted by CaptainBlack
Cyclonical - pertaining to a cyclone, so in this case a curve that spirals (inward if direction has a sense)

Is there more context available?

CB
Yes. The question is,

"A uniform string of weight W rests on a rough cyclonical curve which has its axis vertical and vertex upwards, the string extending from the vertex to a cusp. Show that the least horizontal force applied at the vertex that will cause the string to slip upwards is $\displaystyle\frac{W(3e^{\frac{\mu\pi}{2}}-\mu^2-1)}{\mu^2+4}$, where $\mu$ is the coeffecient of friction."

So to solve the problem we need to know the intrinsic equation (equation which relates arc length to the angle of the tangent) of a cyclonical curve. I think the problem does not give enough details to solve it. For there are many different spirals such as, logarithmic spiral, Archimedean spiral etc. What is your idea?