I have my own concept question. Ignoring air friction and mass of string, and only considering the motion of the bottom right quarter of a circle, where only gravity acts on the mass. Lets say I have a mass attached to a rope with length R. I hold the string in my left hand and the mass in the other hand. I let go the mass so it will fall in a circular motion and be vertical at the bottom my left hand. Now I have a yo-yo with the same mass and with initial R as well. I do the same thing with the yo-yo as I did with the first mass. The yoyo will be changing length as it falls. Will the yo-yo and the first mass take the same time to reach the bottom? I'm guessing yes because they have the same tension and only force acting on it is gravity. Meaning, they will have the same velocities.