Q: given angular velocity, time and radius how to you figure distance along the perimeter? Answer: To find a distance we need a rate (speed) multiplied by a time. The tangential speed is given by the angular velocity times the radius (1) v = wr where w = angular velocity and r = radius. The distance along a perimeter (of a circle) is the tangential speed times time. (2) d = vt where d = the distance along the perimeter v = the tangential velocity defined in (1) above t = time Substituting for v from (1) in the formula for distance (2) gives ************* (3) * d = wrt * ************* Note: If the angular velocity is in degrees per second first multiply by pi (3.14159...) and divide by 360 to convert w to radians per unit time. Note: if w is not constant then the above is not true. We must replace wt in formula (3) with an intrgral over time from 0 to t. / d = r| w dt / Q: given the straight line velocity, time and radius how to you figure distance along the perimeter? Answer: I will assume that you mean the tangential velocity when you say straight line velocity. In this case distance is just the straight line velocity times the time and radius is not needed! d = vt Where d = distance v = tangential velocity t = time. If v is variable with time then you have to do an integral. / d = | v dt / note: When text books speak of velocity they usualy mean a vector quantity but in the context of uniform circular motion they are usualy talking about tangential speed. note: I am a little suspicious about the wording of this question. I wonder if what you really are asking about is angle? If so the you can get the angular velocity w by dividing v by r w = v/r the angle in radians swept out by an object moving along a circle will be angle = wt where t is time. Substituting v/r for w in the above equation then gives angle = (v/r)t