Two identical uniform bars are held on a horizontal surface by sliding a vertical peg through their centers as shown above. In both cases, objects of equal mass slide with negligible friction toward the bars with equal speeds. In Case 3, shown above left, the object collides and sticks to the bar, and in Case 4, shown above right, the object bounces off the bar and reverses direction.

Question

Immediately after the collision, is the magnitude of the resulting angular momentum of the bar about its center of mass greater in Case 3, greater in Case 4, or the same for both? Justify your answer.

Answer 1

The magnitude of the resulting angular momentum of the bar about its center of mass is the same for both Case 3 and Case 4. This is because angular momentum is conserved in both cases. In Case 3, the object collides and sticks to the bar, so the angular momentum of the object is transferred to the bar. In Case 4, the object bounces off the bar and reverses direction, so the angular momentum of the object is reversed and the bar does not gain any angular momentum. Therefore, the magnitude of the resulting angular momentum of the bar about its center of mass is the same for both cases.