Q: Two identical uniform sticks are rotating about their stationary centers with equal angular speeds. The vertical stick is slowly raised until its top end collides with the center of the horizontal stick. The sticks join together to make a rigid object in the shape of a T. Assume that the collision takes place when the top stick lies in the plane of the paper. Immediately after the collision, one point (in addition to the CM) on the T will instantaneously be at rest. Where is this point?
I was thinking that when/where they collide, their rotations would be in opposite directions, and so would cancel out and make the instantaneously still point the point of connection. Is this not correct? How could one prove or disprove this analytically/mathematically? Besides just thinking about it or visualizing it, I'm not sure how to go about this problem. Could anyone offer some guidance?