Uniform Circular Motion confusion.

[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.

 

[Doc Al]

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

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.

 

[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 $$\omega$$.

I'm still scratching my head.

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...

 

[Doc Al]

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

Makes no sense to me. What textbook is this?

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

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: $2 \pi r \omega$.

 

[DavidAlan]

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