Pen Falling Off a Finger
To see the movement of the centre of mass of a pen falling off a finger see this mathematica demonstration centre of mass motion.
This is a fairly complex simulation that requires some playing with it to make sense of what it is telling you. As a first step, make sure you read the details of what the various parameters mean. Then I sugges that you set the slider controld to a pen oriented vertically up (so no angle or velocity to start with) and change just one of the sliders. Try and make sense of the traces of the pen’s position at time intervals (the coloured lines) and the traces of the ends (the black lines).
There’s some odd behviour that you can visualise here. Pens falling off fingers may seem ordinary, but under certain conditions they can exhibit extremely unpredictable behaviour. More of that at the end of the course, as we end up in S6.7