# Axis of rotation of a rod after colliding with a mass

Considering a rod AB lying on a frictionless horizontal surface, it's mass being M and length being L. A mass m strikes the rod at end A with a velocity v and perpendicular to AB and the mass comes to rest immediately after collision.

Now, here I have two questions.

1. I know the center of percussion of a hinged rod is the point at which if a horizontal impulsive force is applied, there is no reaction at the pivot. But, in my case, there is no pivot (the rod is unhinged). About which axis does the rod start rotating just after collision? Is the about the axis passing through the center of mass perpendicular to the place of the horizontal surface, or the center of percussion, perpendicular to the plane of the surface?

Is the center of percussion at rest and the axis of rotation immediately after the collision?

1. Would the axis of rotation, or the distance of the center of percussion of rod (2L/3) change if the mass m stuck to the rod?
• Are you familiar with the laws of conservation of linear momentum and conservation of angular momentum? If so, have you applied them before? Jun 25, 2021 at 16:26
• @Chemomechanics Yes I have. But here angular momentum can be conserved about any axis as there is no net torque. I know how to solve these questions, I only have the doubts regarding the center of percussion Jun 25, 2021 at 16:27
• As no pivot exists in this problem, I'm not sure why the center of percussion is relevant. Jun 25, 2021 at 16:36