How to Apply Conservation of Angular Momentum to Rotational Motion and Collisions

Here is a sliding block and hanging rod, where the block collides and sticks to the rod. Angular momentum is needed, and here is a case where conservation of angular momentum is used to figure out the initial speed of the block before the collision occurs. Take a look to see the general, symbolic setup for such a problem, which will be similar to a ballistic pendulum from linear momentum days. I hope this helps.

How to Use the Parallel Axis Theorem to Find Moments of Inertia

The parallel axis theorem is a neat shortcut that allows us to find moments of inertia for objects when the axis of rotation is somewhere other than the center of mass of the object. If you know the inertia for objects when going through the center of mass, you can quickly find the new value of I for any axis that is parallel to the center of mass axis and displaced by some distance from the center of mass, d. The theorem says I_new = I_cm + Md^2. We do not have to use the integral to apply the theorem, which is why it is such a nice shortcut.

This video shows a couple quick examples of how to apply the theorem. Hope it helps!