The main idea with these problems is that a particle comes in at a straight line and collides with another object that then results in rotation. Think of a ball of clay being thrown at a baseball bat being held out. The ball, moving in a straight line, hits the bat and causes the bat to rotate. The bat could either be fixed at some point that the new clay/bat system will rotate around or the bat could be unattached and free to move unrestricted and then the clay/bat system will rotate around its new center mass.
Below is a good video talking qualitatively about what happens when a linear moving particle collides with an object that is free to rotate
Next is a video that show the process of solving a collision problem between a moving particle and an object that is free to rotate

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