Uniform circular motion; radial and lateral components?

[Signifier]

Hello, I'm trying to understand circular motion more intimately. Let's say I have a 1.8 m long piece of twine that I attach to my ceiling and attach a rock with a mass of 650 g from the hanging end. Let's say (with my superhuman coordination) I manage to get the rock spinning in a perfectly horizontal circle (IE it doesn't move up or down in the z-axis at all) at a constant speed. If I know the angle the twine makes with the ceiling, is there a way to calculate the speed the rock is going around the circle at?

Here are my initial thoughts. Once the motion has started and the rock is in its perfect circle at its constant velocity, let's say it makes a constant angle theta with the ceiling. Doing a little trig, the radius of the circle the rock is traveling in would be equal to 1.8sin(180 - theta) m. If we ignore drag and other neg. forces, then three forces are acting on the rock: gravity, tension, and a centripetal force. It is at this point that my whole body starts shaking and I generally pass out.

In this ideal situation, the angle the string makes with the ceiling would be a function of the velocity the rock is traveling around the circle in and therefore the velocity the rock is traveling around the circle in would be a function of the angle. I have come up with two formulas for the rock's velocity, but in both mass disappears so they obviously can't be right.

I would appreciate any help - or at least perhaps a site covering uniform circular motion a bit better than the two pages my textbook gives it. Thank you!

 

[d_leet]

then three forces are acting on the rock: gravity, tension, and a centripetal force. It is at this point that my whole body starts shaking and I generally pass out.

Actually only two forces are acting on the rock, the tension from the string and the weight of the rock. The centripetal force on the rock comes from a component of the tension in the string and is not a separate force from it.

 

[Signifier]

That is interesting... could you explain what you mean by the centripetal force coming from a "component of the tension in the string"?

 

[d_leet]

Well centripetal force isn't a new kind of force, it has to come from something, I'm not sure how to word this so this probably isn't exactly what I mean or want to say, but I hope you get what I mean. The tension holding the ball in a circle is at an angle right? Yes, so there are two components to it one horizontal and one vertical, assuming the ball is in equilibrium in the vertical direction the upward tension has to be equal to its weight, but we know that the ball is in uniform circular motion in the horizontal direction, well that circular motion has to be caused by some force since the velocity of the rock is changing it must be accelerating.

Ok to depart from that for just a second, the two requirements for a force to be centripetal are that it is perpendicular to the velocity vector and towards the center of motion. Now since the horizontal tension in the strings fits these criteria it is a centripetal force that acts on the ball.

The key thing is that the centripetal force on the ball is not a separate thing from the tension in the string, just a component of it.