Overall, the problems I know when to use it are when there is something like a rotating pulley disk which has a string wrung around it and a block at the end falling down. Another place I know when to include it is when there is a ball rolling down a hill, and I need to take into account rotational and translational kinetic energy.
However, there are some instances where I don't understand why they include it. For example, if there is a rotating disk with radius $R$ at rest, and I glue a point mass to the side, and it asks for the angular velocity of the disk when the point mass reaches the bottom. In this case, should we include rotational and translational kinetic energy?
