Suppose my system involves:
1) A mounted wheel with some outward flap
2) A bullet already in motion
Initially the net angular momentum is 0 and the net kinetic energy is just that of the speeding bullet.
The bullet hits the flap, causing the wheel to turn, and continues on (slightly slower).
Now the net angular momentum of the system is > 0 and the net kinetic energy is lower.
1) Is energy being converted into angular momentum here (so net energy is conserved)?
2) How is the net angular momentum of this system being conserved with the net amount before/after has changed?
Best Answer
I'll address one underlying issue.
It's important to remember that objects moving in straight lines can have angular momentum. Your bullet can, for example.
The definition of angular momentum $\vec L$ for some point object is:
$$\vec L \equiv \vec r \times \vec p.$$
In that definition, $\vec r$ is the position vector of your object and $\vec p$ is the momentum of the object. So as long as the cross product of the position and momentum vectors is non-zero, something moving in a straight line can have angular momentum.
Now, there are other expressions for angular momentum. You may have seen $\vec L = I \vec\omega,$ which is quite useful for spinning objects. This is actually a special case that can be derived from the definition above.