Angular momentum works almost like linear momentum. If an object is spinning, it is said to have some amount of momentum that is based on its rotational inertia and its angular velocity (similar to mass and linear velocity for linear momentum). Angular momentum (L) is defined as:
L = Iw
As you can see, it is very similar to the linear momementum equation, p = mv. For a spinning point particle, the angular momentum is:
L = mvr
Just like linear momentum, angular momentum is always conserved as well when there are no external forces acting on a system. This is why skaters spin faster when they bring their arms inward. Bringing their arms inward decreases their rotational inertia, and since angular momentum must be conserved, angular velocity increases.
In another case, if we have two spinning disks spinning at different rates and then join together to spin at the same speed, the angular momentum will still be constant. For example, disk A is spinning at 3 s-1 and B is spinning at 5 s-1. Disk A has a mass of 9 kg and has a radius of 0.30 m. Disk B has a mass of 4 kg and has a radius of 0.20 m. Let’s figure out what happens when they come together:
Lbefore = Lafter IAwA + IBwB = (IA + IB)wafter
If you plug in all the values, you eventually will find out that the two disks joined together spin with an angular velocity (wafter) of about 3.3 s-1.