Why is the radius of a twirling rope represented by Lcostheta instead of r?

[indelible.eggs]

I'm having difficulty understanding why the radius is not represented by r, but Lcostheta , isn't the entire rope in the horizontal direction? There is something I'm missing. Thanks. (Hopefully I posted this correctly.)

Homework Statement

The problem is example 1 on http://physics.bu.edu/~duffy/py105.html
You have to click on Circular Motion on the left-hand side of the site.

Homework Equations

F=mv^2/r

The Attempt at a Solution

It has already been solved on the web site.

 

[voko]

The example indicates quite plainly that the rope is not horizontal, but at an angle. Do you not understand why this is so?

 

[indelible.eggs]

Perhaps I'm having difficulty understanding what is being described. The rope is at an angle twirling some object in a horizontal circle. I understand why the tension would need to be broken down into its components. But it seems that the radius of the horizontal circle is purely horizontal (even if the rope is not) thus the radius would be r. I suspect I'm asking a very simple question, but I'm just not getting it. Thanks

 

[indelible.eggs]

I think I understand now: We have the length of the rope so the radius of the rope can be described as the horizontal component of the length of the rope. Thanks for your help, it was hard for me to see.

 

[voko]

Yes, your current understanding is correct. r is indeed the "horizontal component" of the rope.