Rotation and phase difference

I use this experiment to show the phase difference in cyclical motion. I rotate the turntable and the shadow of the ball moves from the middle to the side, back to the middle across to the other side and back to the middle. If we set up a pendulum as well, its shadow would move in the same way. So motion is a circle is linked to pendulum motion, and is linked to wave motion, because waves go middle to side to middle to other side and back to middle. One quarter of a rotation moves the shadow from the middle to one side. So I say that the phase difference between the middle and the side in a wave motion is 90 degrees or pi/2 radians. Half a rotation will bring the shadow back to the middle but it will be moving in the opposite direction. So the half way point in a wave motion is 180 degrees or pi radians out from the starting point.