What is a function that describes motion in a circular path?

[LearninDaMath]

If an object is moving in a perfect circlular path, what function(s) describe its path as a function of time?

 

[vivekrai]

It could be \vec{r}\cdot\vec{v} = 0 or even x^2+y^2=r^2.

r = Position vector, v = Velocity vector.

 

[Redbelly98]

It could be \vec{r}\cdot\vec{v} = 0 or even x^2+y^2=r^2.

r = Position vector, v = Velocity vector.

None of your expressions contain time as a variable, as requested in the OP. That being said, we shouldn't give things away without LearninDaMath showing some attempt towards answering the question.

 

[LearninDaMath]

None of your expressions contain time as a variable, as requested in the OP. That being said, we shouldn't give things away without LearninDaMath showing some attempt towards answering the question.

Please see thread https://www.physicsforums.com/showthread.php?t=580771 Post #8-16 for thorough attempt and on-going progress on this topic. Rest assured no information is being given away without effort on my part. I appreciate the expertise of physicsforums members who take some time to help out those of us who are learning the basics of various subjects and, within this or any of the threads I have created, it would be inaccurate for anyone to accuse anyone of trying to simply receive or provide answers without a fair reciprication of effort.

This is my first time logging into and visiting physicsforums since Feb 25. I have had a very tough work schedule this weekend. But I am not finished exploring the topic of this thread. It is not a specific homework problem. Nor am I seeking an answer to a specific homework problem. This section of physicsforums is for homework problems, homework related problems, or anything related to textbook style questions.

Thank you for your concern, but there is nothing to worry about here. If you feel it's absolutely necessary, you could combine this thread into the thread I cited above (although that would make the other thread more confusing to read through.) Or, just remove the warning on this thread since this question is not a specific homework question. Or leave the warning as is so it can serve as a reminder that I should thoroughly preface each thread with whether or not it is a homework problem or not. Perhaps I should have referenced the above thread when making this thread to avoid this confusion. As soon as I can get back to this physics topic, I will continue it. Right now, I have to concentrate on Calculus. Sorry for any confusion.

Thanks, respectfully,
LearninDaMath

 

[SammyS]

If an object is moving in a perfect circular path, what function(s) describe its path as a function of time?

The functions usually used are sine and cosine.

(Not giving too much away!)

 

[LearninDaMath]

The functions usually used are sine and cosine.

(Not giving too much away!)

Thanks, could you provide some insight into this: https://www.physicsforums.com/showthread.php?t=582325

 

[Redbelly98]

The functions usually used are sine and cosine.

(Not giving too much away!)

FYI, LearninDaMath has actually made considerable headway on this question:

Okay, here is what I have so far:


The equation of a line is x^{2}+y^{2} = r^{2}

And the trig identity for a circle is cosθ^{2}+sinθ^{2} = 1

so x = cosθ and y = sinθ

or as a function of time, x(t) = cost and y(t) = sint

However, I'm not sure whether those would be the position functions or if

x(t) = cos^{3}t and y(t) = sin^{2}t

I'm leaning toward the latter since it more resembles the circle equation.

Or... i could be going in a completely wrong direction here.

Assuming I'm heading in the right direction, I still can't figure out how I would use those x and y component functions to actually graph a circle.

 

[LearninDaMath]

Redbelly, thanks. At the time of making this thread, I had made so much progress with gneill in the prior thread, that our discussion was starting to move beyond the content of the original post of that thread. Didn't know if the progress was supposed to continue in the same thread or if a new thread should be made so as to stay on par with the title of the thread so that anyone else searching for the same questions in the future would find the info easier. However, I'm content with the flow of information in the other thread and there seems to have been no direct need (for me) to create a new thread other the search engine convenience for others that I've just described. I will be more descriptive in my original posts in the future.

 

[NascentOxygen]

If it's rotating at a steady rate, then θ ∝ t
⇔ θ = k.t

and you know x = r.cosθ
etc.