# Uniform Circular Motion confusion.

1. Nov 12, 2009

### DavidAlan

How can v = 2$$\pi$$r$$\omega$$?

I've looked at this a hundred different ways... I've found that v = 2$$\pi$$r2$$\omega$$ only.

2. Nov 12, 2009

### Staff: Mentor

You'll have to give us at least a hint of what you are talking about. :tongue:

Please explain the problem you are trying to solve and what your equations are describing.

For uniform circular motion of radius r, the tangential speed v (measured in m/s) is related to the angular speed ω (measured in rad/s) by the formula: v = ωr.

3. Nov 12, 2009

### DavidAlan

The issue arose in the following problem;

A very small cube of mass m is placed on the inside of a funnel rotating around a vertical axis at a constant rate of v revolutions per second. The wall of the funnel makes an angle $$\theta$$ with the horizontal. The coefficient of static friction between cube and funnel is $$\mu$$s and the center of the cube is at a distance r from the axis of rotation. Find (a) largest and (b) smallest values of v for which the cube will not move with respect to the funnel.

I consulted my handy dandy solutions manual and it wanted to work with the assumption that speed in this case = 2 $$\pi$$ r $$\omega$$.

The purposes of defining the speed in this way is to get that F = 4 $$\pi$$2 m r $$\omega$$2.

Sorry for the ambiguity, I thought that someone would recognize the issue right away.

BTW, I don't know what's up with the editing but pi and omega are not powers. They just look that way...

4. Nov 12, 2009

### Staff: Mentor

Makes no sense to me. What textbook is this?
That's because you're mixing Latex and regular text. Try doing it all with Latex, like this: $$2 \pi r \omega$$. Even better is to use 'inline' latex, using the 'itex' tag: $2 \pi r \omega$.

5. Nov 12, 2009

### DavidAlan

It's from Resnick Haliday and Krane 4th edition volume 1.