Spinning Things

Conservation of momentum (previously discussed) can be extended to spinning things. When something spins in place, the object as a whole is not going anywhere, but the individual bits (each with some small mass) are moving at different speeds around the axis, with bits going faster the farther they are from the center. Conservation of momentum applies to each of those bits, so it also applies to them all together. When we talk about this summation of momentum in a spinning situation we call it angular momentum and give it the symbol, L.

So L = I x Ω, where I is a measure of the thing’s shape. If there’s a lot of the thing far from the spinning axis, I is big. Ω is how fast it’s spinning, like ten turns per second.

The cool thing here is that L is constant, so if the shape of the spinning thing changes and I increases or decreases, Ω has to change in the opposite direction.

This is very useful. Think about an ice skater going into a spin. At the start, they have arms way out, one leg trailing way back (big I), and are turning very slowly (small Ω). When they pull their arms and legs tightly in to the center, I gets much smaller, so Ω has to get much bigger - they spin fast!

Let’s see it an action:
Figure skater
Cats falling 
At the playground 
And this guy at taco bell