The Physics of Dance

Sarah Johnston explains the intersection of science and art in dance, and how they play off one another to create a beautifully impressive form


If you’re a dancer trying to improve your technique, the last place you’d go looking for advice is probably a physics textbook. However, dance – like everything – relies on science. Whether you want to jump higher, turn faster, tap louder, or stretch further, there is an underlying scientific principle you are harnessing to be able to move the way that you do. Dancers are often taught techniques which involve using this science without realizing, so I want to shed some light on why we dance the way that we do.

I want to begin with something quintessential to dance, but also to many other artistic sports: turning. If you’ve ever received dance training, you’ve probably heard the same advice about turns: hold your core, move your arms to first position as you turn, and ‘spot’ your head by trying to keep it on the same spot for as long as possible before snapping it round. Each of these things relies on an innate and basic principle of movement mechanics. When we turn, we harness something called angular momentum, which is a measurement of the momentum of a body which is rotating. Angular momentum is a product of the radius of the object (how wide it is) and its linear momentum (which is its mass multiplied by its speed). Momentum must be conserved, it is a physical law of the universe. This means if you change the radius of the object that is spinning, the speed of the object must change to keep the momentum constant.

This can be demonstrated very easily at home using a spinning office chair. If you sit on the chair with your arms out to the side holding weights (or bottles of water or cans of soup) and start spinning, and then bring your arms in towards your body, you’ll find you spin faster. Scientifically, this can be explained as you’re reducing the radius of your body, and so if the radius goes down, to conserve the angular momentum, your speed must increase. This same principle is applied in dance. When you prep to pirouette, you start with your arms spread widely, and as you start to turn, you bring them into your body more closely. As shown with the chair experiment, this speeds you up and enables faster turning. The faster you can turn, the more turns you can usually manage to fit in while balanced, and the more impressive you look. So, if you’re a dancer trying to nail a double or triple pirouette, make sure you’re using your arms to your advantage.

Another key aspect of turning well is good balance, which comes down to harnessing your centre of mass and balancing opposing forces. Everyone understands that gravity is a force acting downwards on us: it's what makes our phones drop, our hair lie flat, and us fall over ungracefully in the street. But although gravity acts downwards, when we stand, there is always an equal and opposite force acting upwards from the ground resisting us falling through the floor. This is called electrostatic force, and it’s the reason we can actually stand on things and aren’t just constantly sucked towards the centre of the Earth. When dancers balance, they have to try and get these two forces to be exactly equal and opposite by moving their centre of mass over the leg they are balancing on. This is why you hear a lot about engaging your core or pulling in your ribs when dancing. Contracting your core effectively makes your body into a straight rod, and keeps your centre of mass above your leg so that you can balance. If your centre of mass is not directly above the leg that you are balanced on, the gravitational pull acting on your centre of mass won’t exactly balance with the upwards force from the ground, causing you to fall over. So next time you are wobbling, pull in that core, straighten that neck, and imagine yourself as a metal rod being pulled straight above your leg.

Balancing is not only artistically impressive but is physically impressive because of the huge pressures your body is subjected to when you do it. Pressure is defined as the force per unit area, where the force is due to your mass, and so if the area you are balancing on is small e.g. just the ball of your foot, then the pressure your foot is exerting is incredibly large. Take for instance a dancer standing on pointe. The total area of the pointe shoe is very small, a few 10s of cm2, and if the weight of the dancer is 50+ kg then you can end up with pressures of thousands of Pascals. In fact, a dancer in a pointe shoe can exert more pressure on the ground than a tank, because although the tank is much heavier, its weight is spread over a much larger area. This is why it is so important to have properly fitted dance shoes, to make sure that all of the pressure you’re exerting on the ground doesn’t just break your toes.

I might even go as far as to say that gravity is the worst enemy of dancers. Dancers can make jumps and leaps look effortless, when they are in fact battling against a fundamental force. The gravitational field on Earth is 9.8 Newtons per kilogram, which means that for every kilogram you weigh there are 9.8 Newtons of force pulling you downwards. Gravity only affects vertical motion and works to pull the dance down, so jumps usually look like a parabola (arch) shape if you watch them from the side as the dancer continues to move horizontally while they jump. However, the effect of gravity limits how long they can spend in the air, as it causes them to accelerate back towards the ground. This means dancers need to come up with inventive and artistic ways to increase their ‘air time’ or at least appear to increase it. Sometimes when you watch a dancer, they can create an illusion of floating or hanging in the air. When a dancer reaches the peak of their jump (the highest point), they can tilt their head back and bring only their legs and arms up while keeping their torso steady which makes it appear as though they are still moving upwards. This gives the illusion of them being frozen in the air for a moment, making them seem to float. If you are trying to get a bit of extra height on your jumps, as well as your take-off, make sure you're harnessing your body whilst in the air.

A lot of time forces like gravity can hinder dancers, but there are some styles where you can use the natural forces in the world to your advantage. In tap dance, the sharp tap sounds are made by hitting metal panels on the bottom of the tap shoe off of the ground. Many people think the best way to get a louder, clearer tap is to hit the ground harder by exerting more force through your foot, but a much easier way to do it is to tap quicker. The sound made by my tap shoes is all to do with the collision of the tap shoe with the ground and relies on the principle of impulse. Impulse is the product of the exerted force and the time it is exerted for, and what it tells us is that the amount of impulse an object can give is related to its change in velocity. When tapping, the tap stops when it hits the ground and transfers its energy into the floor, giving off the signature sound (and if you are not careful taking chunks out of your floor too!). This means that if your foot is moving quickly, then the change in velocity is large. If you ‘tapped’ the floor more slowly, you would get a smaller impulse, and so a quieter sound. This is how tap dancers ‘scuff’ or ‘drag’. However, if you kept your foot in contact with the ground for a shorter time, your change in velocity over time would be greater, so you would exert a larger impulse and subsequently make a louder noise. An easy way to show this at home is using a tap step called the pickup. If you put your heel to the floor with your foot flexed and toes in the air, and drag it slowly backwards so your toes touch the floor, there is little to no sound. However, if you take it from the same position and snap your foot backwards so that your toes quickly hit off the ground, then you make a loud tap sound. This shows perfectly how you can use the same force, but at a much larger speed over a shorter time, to get a better noise.

Although I have said gravity can be a dancer’s worst enemy, it can also help. Many stretches in dancing, specifically dynamic stretches, use gravity to loosen muscles without having to force them. One of the most popular stretches that demonstrates this is a wall split. You lie on the floor, with your bum against a wall and your legs straight up in the air. You then slowly let your legs fall open and remain in the stretch they can get to. In this stretch, gravity actually helps to pull your legs downwards without having to push them manually. As I’ve said before, Earth’s gravitational field exerts 9.8 Newtons for every kilogram of weight, so using gravity to help stretch is actually a hugely efficient method because you don’t need to have someone on hand to physically push on your muscles.

So next time you are at a ballet, or a dance show, or even in your own class, do not forget the amazing things physics does to make dance possible. While dance is at heart a creative and emotive art form, it is equally a scientific experiment into our own bodies and how they can demonstrate the fundamental concepts of the world. For me, dance is an amazing melding of the beauty of self-expression and the wonder of science all rolled into one, and I hope now you can see why.