Momentous Holidays

This week's question comes from my nephew Ezra:


How come I have to push my arm out to move?

What you're experiencing is conservation of angular momentum.  Regular linear momentum is given by the mass times the velocity

This is why fast, heavy things are harder to catch than slow, light things – You have to overcome their momentum to make them stop.  Similarly, if you want to get something moving really fast, it pushes back on you to cancel out the momentum you impart to it.  Hence the recoil in firing a gun.

Angular momentum is the same idea applied to things moving in a circle.  The classic example is a figure skater spinning at different speeds, which I've mentioned before, but it applies here too.  When you push your arm out, part of that motion is going around the seat, so it has angular momentum.  That gets transferred to the seat, making it turn in the opposite direction.

Here are two experiments you can try: What happens if you hold your arm out and pull in, instead of pushing outward?  What happens when you push your arm towards the center of the seat, instead of to the side?