Translational and rotational motion

[Tonyt88]

1. A uniform stick of mass m and length l spins arounds on a frictionless horizontal table, with its CM stationary (but not fixed by a pivot). A mass M is placed on the plane, and the end of the stick collides elastically with it, as shown. What should M be so that after the collision the stick has translational motion, but no rotational motion?




2. This is where I get stuck



3. I'm hindered not only because I don't know which equations to apply, but also, I don't know what would result in the stick having just translational motion.

 

[AlephZero]

3. I'm hindered not only because I don't know which equations to apply, but also, I don't know what would result in the stick having just translational motion.[/QUOTE]

What equations do you usually use for problems involving impact? Hint: conservation of ...

If the mass was very light (like a speck of dust) the stick would just knock it out of the way and carry on rotating. If the mass was very heavy, the mass wouldn't move much, but the stick would bounce off and probably it would be rotating the opposite way. Somewhere in between, there is a mass where the rotation after the collision is zero. That's what you need to find.