A uniform rod AC of length l and mass m is kept on a horizontal smooth plane. It is free to rotate and move. A particle of same mass m moving on the plane with velocity v strikes the rod at point B making an angle 37 degree with the rod. The collision is elastic.
I am trying to solve the problem by conserving angular momentum of rod, linear momentum of rod and particle, and energy conservation.
My question is
- Can the angular momentum of Rod be conserved about point B although the point B is accelerated during collision?
- Does elastic collision mean that the Velocity of approach = velocity of seperation about Common Normal through point B?
Best Answer
If you mean B as a point in an inertial frame, then yes. If you mean B as a point attached to the rod, then no. You're correct that if the axis under consideration is accelerating then it makes things difficult. In general, you don't want to do this unless the accelerating axis contains the center of mass of the object you are considering to rotate.
It means that the total mechanical energy of the system (all kinetic in this case) is the same before and after the collision. In a frame where the center of mass is at rest, then the velocities before and after will be the same. In other frames, it may not be. A golf ball and a golf club may have a nearly elastic collision, but the ball will have a very different velocity before and after being struck on a tee.