Confusion in choosing an origin point for angular momentum

[bob012345]

It might help to work out the problem where the rod is not connected to a slider first as a reference answer then ask how the slider changes things. I believe there is a key insight to this problem that makes it simple. Very simple for both cases. Hint: pick any point along a line going through the slider in the direction it slides from -∞ to +∞ and ask what is the angular momentum of $m_1$ around that point?

 

[haruspex]

I think because the slider would do work on the rod because the motion is constrained.

No, it is nothing to do with the slider. There is no friction, so the force the slider would exert is normal to its motion.

What energy is lost is in the impact. If it were elastic then the relative masses of bullet and rod would dictate their relative shares of KE afterwards. Not sure of the details in this case without working through the algebra, but for point masses the relative velocity reverses. So in principle you could figure out how much KE is lost in terms of the given variables. And with the right values of those variables it could be zero.

 

[bob012345]

No, it is nothing to do with the slider. There is no friction, so the force the slider would exert is normal to its motion.

What energy is lost is in the impact. If it were elastic then the relative masses of bullet and rod would dictate their relative shares of KE afterwards. Not sure of the details in this case without working through the algebra, but for point masses the relative velocity reverses. So in principle you could figure out how much KE is lost in terms of the given variables. And with the right values of those variables it could be zero.

Ok but this may be an elastic collision since the end velocity of $m_1$ is zero yet it is not imbedded in the rod.

 

[haruspex]

Ok but this may be an elastic collision since the end velocity of $m_1$ is zero yet it is not imbedded in the rod.

Yes, that's what I wrote: " with the right values of those variables [the lost KE] could be zero."
Looks like it would be mass of rod = 4 x mass of bullet.

 

[bob012345]

Yes, that's what I wrote: " with the right values of those variables [the lost KE] could be zero."
Looks like it would be mass of rod = 4 x mass of bullet.

Just for fun, consider the subsequent motion of the rod. Obviously it will oscillate and overall move left. Assuming no other loss mechanisms we should be able to write the equations of motion.