Uniform Circular Motion confusion.

In summary, the formula for tangential speed in uniform circular motion is v = 2\pir\omega. In the conversation, the issue of defining speed is discussed in relation to a problem involving a rotating funnel and a cube placed inside. The textbook suggests using the assumption that speed = 2\pir\omega, but the person is still unsure about the solution.
  • #1
DavidAlan
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How can v = 2[tex]\pi[/tex]r[tex]\omega[/tex]?

I've looked at this a hundred different ways... I've found that v = 2[tex]\pi[/tex]r2[tex]\omega[/tex] only.
 
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  • #2
You'll have to give us at least a hint of what you are talking about. :-p

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
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 [tex]\theta[/tex] with the horizontal. The coefficient of static friction between cube and funnel is [tex]\mu[/tex]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 [tex]\pi[/tex] r [tex]\omega[/tex].

I'm still scratching my head.

The purposes of defining the speed in this way is to get that F = 4 [tex]\pi[/tex]2 m r [tex]\omega[/tex]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... :blushing:
 
  • #4
DavidAlan said:
I consulted my handy dandy solutions manual and it wanted to work with the assumption that speed in this case = 2 [tex]\pi[/tex] r [tex]\omega[/tex].
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: [tex]2 \pi r \omega[/tex]. Even better is to use 'inline' latex, using the 'itex' tag: [itex]2 \pi r \omega[/itex].
 
  • #5
It's from Resnick Haliday and Krane 4th edition volume 1.
 

FAQ: Uniform Circular Motion confusion.

1. What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves in a circular path at a constant speed. This means that the object covers equal distances in equal amounts of time, resulting in a constant speed along the circle.

2. How is uniform circular motion different from other types of motion?

Uniform circular motion is different from other types of motion because it involves both a change in direction and a constant speed. In other types of motion, the object may have a constant speed but its direction may change, or its speed may change while its direction remains constant.

3. What causes an object to undergo uniform circular motion?

An object undergoes uniform circular motion when it is acted upon by a centripetal force, which is a force directed towards the center of the circular path. This force is necessary to keep the object moving in a circular path at a constant speed.

4. Can an object in uniform circular motion have a changing velocity?

Yes, an object in uniform circular motion can have a changing velocity. Although the speed remains constant, the velocity changes because it is a vector quantity that takes into account both the speed and direction of motion. As the direction of the object changes, so does its velocity.

5. What are some examples of uniform circular motion?

Some examples of uniform circular motion include a car going around a roundabout, a planet orbiting around the sun, and a satellite orbiting around the Earth. Any object that moves in a circular path at a constant speed can be considered to be undergoing uniform circular motion.

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