Final answer:
The principle demonstrated by two kids sliding and grabbing each other on frictionless ice is the conservation of momentum, which states that the total momentum remains constant in an isolated system.
Step-by-step explanation:
The principle of physics demonstrated when two kids slide towards each other on a frictionless surface and then grab on to each other is the conservation of momentum. According to Newton's first law of motion, when no external forces are acting on a system, the total momentum of the system remains constant. Therefore, when the kids on ice grab each other, their individual momenta combine, and the total momentum before and after they come together remains unchanged, despite their individual speeds changing. This entire interaction is an example of an isolated system where external forces are negligible, and the law of conservation of momentum applies.