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January 20

Rotating a point by a distance

What is the term used to mean "rotate a point around a circle by a specific distance"? For example, I have a circle with a radius of 50 inches. I want to rotate a point on the edge of the circle clockwise 2 inches. Everything I find in textbooks and online refers to rotating by a number of degrees or radians, not by a distance. I have found references to measuring the distance rotated after rotating by a specific number of degrees, which is not exactly what I am looking for. 97.82.165.112 (talk) 15:44, 20 January 2023 (UTC)[reply]

So, the reason why radians exist is that radians is a distance, or almost so. For a unit circle of radius 1, the length of an arc of X radians is... X. Radius * angle in radians = length of arc. So if you have a 2 inch arc, on a circle of radius 50, that's an angle of 2/50 = 0.04 radians, or about 2.29 degrees. --Jayron 32 16:57, 20 January 2023 (UTC)[reply]

If the issue is not one of formulas but of terminology, you might say that the point is shifted along an arc of the given circle having a specific length. (The term "distance" may be interpreted in the context of planar geometry as meaning Euclidean distance.) --Lambiam 17:16, 20 January 2023 (UTC)[reply]

Thanks. Searching for rotation by arc length brings up references to converting arc length to radians (as Jayron suggested) and then rotating by the angle. 97.82.165.112 (talk) 18:00, 20 January 2023 (UTC)[reply]