Newton's Second Law of Motion: Newton's second law of motion states that the rate of change of momentum is proportional to the amount of force applied and terms of the object's acceleration. Force equal mass times acceleration. When a dancer does a quick turn, there has to be a great amount of force to complete the turn in time for the next step. The amount of force on the floor used to complete the turn also determines how fast the dancer can get through the turn.
The dancer is using force on the floor to turn completely.
Newton's Third Law of Motion: Newton's third law of motion states that for a action, there's an equal and opposite reaction. In dance, when you're on the floor, you push against the floor to be able to get up. When the dancer pushes, the floor pushes on the dancer equally as hard, allowing the dancer to get back up.
The dancer has to push herself up but uses force to do so. The floor pushes back equally as hard letting her get up.