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I need to find the radius of a circle.

Consider two circles with a common center. The radius of circle #1 is r-d. The radius of circle #2 is r+d. The common center is called O.

A straight arm is rotating around O. Where the arm intersects the two circles we get two points of contact close to each other, p1 (arm in contact with circle1) and p2 (arm in contact with circle 2). You might think of p1 and p2 as the coordinates of the front wheels of a car driving around in a circle.

What is known is the instantaneous velocity (ds/dt) of the two points p1 (velocity v1) and p2 (velocity v2) in their orbit around the common center O. The distance between the two points is also known, it is 2d. I need to compute r.

Since I know v1 and v2 I can compute the quota q=v1/v2. I figure that from this quota and d it should be possible to compute the radius r. A smaller q with constant d should (I think) give larger r. A constant q with smaller d should also give larger r.

If, for example, v1 is 10 m/s, v2 is 10.001 m/s and d is 1 mm, what is the radius of the circle?

I would prefer a simple equation with r on one side of the = and v1, v2 and d on the other, if possible.

This obviously beats me, so please show me how to compute r.

Consider two circles with a common center. The radius of circle #1 is r-d. The radius of circle #2 is r+d. The common center is called O.

A straight arm is rotating around O. Where the arm intersects the two circles we get two points of contact close to each other, p1 (arm in contact with circle1) and p2 (arm in contact with circle 2). You might think of p1 and p2 as the coordinates of the front wheels of a car driving around in a circle.

What is known is the instantaneous velocity (ds/dt) of the two points p1 (velocity v1) and p2 (velocity v2) in their orbit around the common center O. The distance between the two points is also known, it is 2d. I need to compute r.

Since I know v1 and v2 I can compute the quota q=v1/v2. I figure that from this quota and d it should be possible to compute the radius r. A smaller q with constant d should (I think) give larger r. A constant q with smaller d should also give larger r.

If, for example, v1 is 10 m/s, v2 is 10.001 m/s and d is 1 mm, what is the radius of the circle?

I would prefer a simple equation with r on one side of the = and v1, v2 and d on the other, if possible.

This obviously beats me, so please show me how to compute r.

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