# What is the physics behind a pirouette?

Around last week, I watched a ballet production at the Melbourne Arts Centre, and boy was I amazed! These people dressed up in costumes were spinning on their toes in all kinds of ways, and I was wondering how they did it; i.e. what were the physics behind it.

It's called a pirouette, I think, and I went here to learn more about it. The lady there says that males in particular can do up to ten pirouettes, and as the lady demonstrates, this is done on her toes. She also says that the number of turns one does depends on the skill of the dancer. This is not specific and does not give information on the physics behind the pirouette.

I know there must be centripetal force created. She said the arms open up, and as she turns, she closes them again, so this must be a drive for momentum. Her right leg is also turned outwards with her foot to her knee (some position called passe) so this might also cause momentum if she is pushing her knee back (which is what it looks like to me). Otherwise the lifted knee would send her leaning towards where it is, but when she turns, she is perfectly straight.

However, bringing the arms together and her foot on her knee concentrates a lot of force on just a small base area to work with; that is, the toes. Also, wouldn't torque be playing a role here?

If you get a rag and hold it from both ends, it will be pretty loose; but if you stretch it and try to move it, it will be tight and rigid. Maybe the ballet dancer is doing that to control torque? Pushing downwards and lifting upwards at the same time? Newton's third law?

Also, why does she start in fourth position for a pirouette? How does she know how much momentum to apply for one and two pirouettes? Why can males do ten?? That's crazy! Does this mean males are more skilled than females?

I think a key thing here is weight distribution. This would make a lot of sense, but I am not too sure.

What is the physics behind a pirouette?

If you google "physics of pirouettes" a number of articles come up for individual figures, and you could accumulate a knowledge base.

The basic physics is the physics of walking and staying upright: energy provided by chemical reactions in muscles, momentum provided by force generated vectorialy by muscles , friction with the ground changing vectors by the opposing dp/dt, and the corresponding momentum and angular momentum conservations.

We instinctively use angular momentum to balance when turning and to avoid falls every day.

Why can males do ten?? That's crazy! Does this mean males are more skilled than females?

Note the energy supply by the chemistry of the body: males are more massive, thus have more energy stored in body. In addition having evolved from hunters their stamina is different from the women who evolved as gatherers :).

Basically, people are made out of stuff, which moves around in space, and people can exert some control over those movements.

Using the conservation of angular momentum to turn spin oneself around quickly is pretty common; figure skaters show it off even more dramatically. The dancer in the video you linked isn't actually moving much faster than you or I do in our daily lives, so she doesn't need to pull her mass in very tight.

A dancer would also experience some gyroscopic effect. This is what keeps a top upright while it's spinning, but (I'm pretty sure) a practiced human could balance on their toes for the duration of a pirouette without spinning around in circles, so it's hard to say how strong or important gyroscopic forces are in this situation.

If your interest is in being able to do a pirouette yourself, learning the physics of the action on paper won't help. You need the strength (and pain tolerance) to balance on your toes, and you need to train your cerebellum to handle the physics subconsciously. A dance instructor, or (to a lesser degree) just fooling around in your bedroom, will help with both of those.