A particle of mass m strikes elastically, a rod of mass M...

A particle of mass $m$ strikes elastically, a rod of mass $M$ and length $L$ suspended from a fixed support, then:
(a) conservation of linear momentum can be applied
(b) conservation of angular momentum can be applied
(c) both the above
(d) none of the above

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Key Concepts

Conservation of Linear Momentum

Linear momentum is conserved in a system when no external net force acts on it. In collision problems, if there are external forces (like the reaction force from a fixed pivot), linear momentum in the system may not be conserved because these forces can impart additional momentum. This must be carefully assessed in collisions involving objects with constraints or supports.

Conservation of Angular Momentum

Angular momentum can be conserved about a chosen pivot point if the net external torque about that point is zero. In systems where a rod is hinged or suspended from a fixed support, while linear momentum may not be conserved due to external forces, angular momentum about the pivot could be conserved because the forces exerted by the support do not typically generate a torque about that point.

Fixed Pivot and Reaction Forces

A fixed pivot introduces external forces which often prevent the conservation of linear momentum during collisions. However, since these reaction forces act at the pivot, they do not produce a torque about that point, allowing for the conservation of angular momentum. This concept is crucial when selecting the appropriate conservation law for solving collision problems involving fixed supports.

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