Physics in Ballet

I have been a dancer for my entire life, however I have never, until this point, stopped to think about the physics behind some of the most fundamental dance moves. Physics is not only able to explain the precise technique needed to achieve certain movements, but also helps explain why a specific body type tends to be seen in professional dancers (mostly ballet). We can easily examine the physics of turns – how to get moving and stay moving, as well as change speed. A common type of turn in ballet is a fouette turn, the progression of which is shown below. 

In order to get turning (position 1), the dancer applies a force to the floor, causing friction to push against the foot in the opposite direction, creating torque. This external torque is responsible for starting the turning motion. The motion of a fouette turn is to move the leg and arms in and out at a specific time (position 2 to position 3), decreasing and increasing speed, respectively. When the turn is first initiated, the dancer pulls their legs and arms close to their body. The purpose of this is to decrease moment of inertia and which would lead to a high rotational velocity. While the dancer is turning, no external torque is acting so rotational momentum is conserved. Moving the legs and arms outward (position 2) slows the dancer down for a moment, because inertia is temporarily increased. Pulling the arms and leg back in (position 3) decreases inertia again and speeds up the turn. This sequence is repeated as many times as desired. Since inertia is proportional to mass of an object, decreasing mass is an efficient way of increasing rotational speed. This is (one of the reasons) why professional ballet dancers all have a very slender figure. Another, perhaps healthier, way to decrease inertia is to work on holding the leg and arms tight to the body, decreasing the radius component of inertia. Often times dancers use a combination of both of these methods in order to obtain the highest rotational speed in turns.