Uniform circular motion proportionalities

In summary, the conversation involves discussing the relationship between frequency of revolution and various factors such as centripetal force, radius of the circular path, and mass of the object. Three graphs are sketched to illustrate this relationship and the proportionalities between frequency and the variables are found. An equation for frequency in terms of tension, radius, and mass is derived and compared to a given equation. The investigation also involves drawing a free body diagram and discussing how it relates to Newton's laws of motion. The thread also includes a request for help and clarification on certain points.
  • #1
MiniTank
62
0
I have a lab with which I am having some major difficulties.

(a) Whats the relationship between frequency of revolution and
- the magnitude of the force causing the circular motion(centripetal force)?
- the radius of the circular path?
- the mass of the object?
(b) Sketch three graphs to illustrate your answer to (a)
(c) Find the proportionalities between frequency of revolution and the variables in (a)
(d) cominge the three results from (c) to obtain the equation for frequency in terms of the tension, the radius, and the mass. check your equation using your data points
(e) The following relationship gives the magnitude of the net force causing the acceleration of an object in uniform circular motion:
[tex]\SigmaF = 4\pi^2mrf^2[/tex]
Rearrange this equation to isolate the frequency. Compare this result with the equation you derived in (d). Indicate the likely causes for any discrepancies.
(f) Draw a FBD for the rubber stopper***
(g) Explain how this investigation illustrates all three of Newton's laws of motion.

***the rubber stopper is attatched to a string which goes through a hollow tube which is attached to weight .. you twirl the stopper from the tube

Heres what I know
(a) the frequency and radius have an inverse relationship
.. the other variables I am not sure
(b) i know what the graph looks like for radius:
|
|
|
\_________
.. something like that
(c) same as above
(d) I need help with
(e) I can rearrange the equation to:
[tex]f=\sqrt{\frac{\SigmaF}{4\pi^2mr}}[/tex]
the next part is hard to do without (d)
(f) I think it has a Tension force going to the left or right, and a Force of gravity, not sure.
(g) Could maybe figure this out after knowing the other answers.

If you need my results just ask, but I doubt you do.

Thanks

BTW i know its a lot but any help would be appreciated.
 
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  • #2
could someone delete this thread .. i accidentally pressed post instead of preview.. thanks
 
  • #3
Delete it yourself by clicking edit and selecting the first options.
 
  • #4
i want to delete the whole thread, not just the post... b/c it is a re-post .. the proper one has the same title .. you can't delete threads
 

FAQ: Uniform circular motion proportionalities

1. What is Uniform Circular Motion?

Uniform circular motion is the motion of an object moving in a circular path at a constant speed. This means that the object covers equal distances in equal time intervals, and its velocity is always tangential to the circular path.

2. What are the proportionalities involved in Uniform Circular Motion?

The proportionalities involved in Uniform Circular Motion are the radius of the circular path, the speed of the object, and the centripetal force acting on the object. The radius is directly proportional to the speed squared, and the centripetal force is proportional to the mass, speed squared, and inverse of the radius.

3. How do these proportionalities affect the motion of the object?

These proportionalities determine the magnitude and direction of the centripetal force required to keep the object in its circular path. As the speed or radius increases, the centripetal force also increases, making the object move faster or in a larger circle. Similarly, a decrease in speed or radius results in a decrease in the centripetal force and a slower or smaller circular motion.

4. Are there any real-life examples of Uniform Circular Motion?

Yes, there are many real-life examples of Uniform Circular Motion, such as a car driving around a roundabout, a satellite orbiting the Earth, and a roller coaster moving around a loop. Any object moving in a circular path with a constant speed is an example of Uniform Circular Motion.

5. How do we calculate the centripetal force in Uniform Circular Motion?

The centripetal force can be calculated using the formula Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the speed, and r is the radius of the circular path. This formula can also be rearranged to calculate the speed or radius of the object in Uniform Circular Motion.

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