Particle colliding completely inelastically with a sphere placed on the floor I'm thinking about the problem of a moving particle colliding completely inelastically with a sphere. The aim is to find the vertical component of velocity of the centre of mass of system after collision.
The sphere is placed on a frictionless floor. The particle is moving horizontally and is aimed above the centre of mass of sphere.
What i know: I know how to do this problem if there is no floor or gravity. Looking at the problem in centre of mass frame, we know that there will be pure rotation about centre of mass of the system.
When we have the floor, the point of the sphere in contact with floor can't have a velocity component perpendicular and downwards(which would be the case if there was no floor).
What i don't understand: I'm not understanding how to incorporate the floor constraint in this problem. The angular momentum won't be conserved about the centre of mass of system because there is a rotational impulse due to normal force at the point of contact with the floor.
Core Question:  I thought that maybe the point of the body in contact with the floor has zero velocity component in the perpendicular direction.
But then, why can't the bottom-most point in contact with the floor has a velocity component in the vertically upwards direction? What's the physical principle involved?

 A: 
But my question is, why should the velocity of bottom of sphere be zero in vertical direction. Why can't it be vertically upwards. What's the physical principle involved here?

It can be vertically upward.  Nothing would prevent it.
But your question says that (in the absence of the floor), the rotation would otherwise give the bottom of the sphere a component in the downward vertical direction.  This is not allowed.
Instead, as the sphere starts to rotate around that point, the normal force from the floor increases to prevent the motion.  This force will be sufficient to prevent the bottom of the sphere from accelerating downward.
Assuming you can calculate the impulse to prevent the sphere from intersecting the floor, then you can calculate the effect on the center of mass of the system to see what the velocity will be immediately after the collision.
For collisions like this, you can assume they happen so quickly that the gravitational effects are small.  In the limit that the impulse happens instantaneously, gravity doesn't matter at all.
