Uniform Circular Motion on a Vertical Circle

Drag M around the circle to see exactly where your hand needs to be at all times to pull M in a perfect circle around the origin at uniform speed using a fixed-length (equal to the radius of the circle M moves around) string. A point mass can be pulled in uniform circular motion. At minimum speed, the hand pulling the mass M in a circle of radius R using a string of length R has to instantaneously move horizontally a distance of 2R but at any higher speeds the hand instead makes a very rapid swing down through the center of the circle and back up to the opposite side.