# Thread: Center of the Circle Path

1. ## Center of the Circle Path

If a circle of radius 2 is made to roll along the x-axis, what is an equation for the path of the center of the circle?

2. Does it seem reasonable to you that the radius of a circle remains constant?

A good question

Move the red point to see the "shape" it makes.

You really should have been able to do this in your head.
$\displaystyle Q_{u^{i_{c^k}}}$

4. ## ok

Can you help me?

5. Originally Posted by symmetry

Can you help me?
As the circle rolls there is always a distance equal to the radius between the edge of the circle and the center. So what is the position of the center of the circle as it rolls on a horizontal surface?

Hint: The answer is in the statement above. If you aren't seeing it, you are thinking about the problem too hard. If it helps, take a can and roll it on a table and see what the center of the can does.

-Dan

6. Originally Posted by symmetry

Can you help me?
I thought the diagram made it pretty clear

Did you try moving the red point (just click and drag, and the circle will roll across the "table")

7. ## ok

Dan,

I guess the answer is right in the question.

Thanks!

8. Originally Posted by symmetry
Dan,

I guess the answer is right in the question.

Thanks!
I want to make sure you've got it. What is your equation for the center of the circle?

-Dan

9. ## ok

Thank you all for your replies.

To Quick:

To Dan:

The equation is y = 2 because the center of the circle makes no vertical movement, right?

10. Originally Posted by symmetry

To Quick: