Science of the arts 2K17

Aim:  I want find out what forces are acting on a dancer's body,  I also want to find out if dancing actually does improve brain power.

Research:  In a word, dance can improve brain power. Dancing opens up new neural pathways. Neural pathways are what basically create memories and process remembering things. The neurons are cells that take up and process information through the electrical and chemical signals. In order for human beings to be able to react to their environment, neurons attract stimuli which is a detectable change in the internal or external environment. For example, the burning of a finger at a candle flame, is transported by the ascending neurons to the central nervous system and in return, the descending neurons to stimulate the arm in order to remove the finger from the flame.  Dancing also improves blood flow to the brain causing you to remember things better and just improve brain power in general.

Forces and motion  The forces on dancers when they are dancing ballet...

- Gravity (downwards)

- Support from the floor (upwards)

- Friction from the floor (sideways)

(The frictions is the force that resists relative motion between two bodies in contact)

Spin forces

-  Angular velocity (how fast an object or person spins).

-  Rotational inertia (the inertia of a rotating object). An inertia is a property of matter when it remains at rest or in motion in the same straight line unless acted upon by some external force. To put it simply it's a tendency to not move or change.

-  Angular momentum is rotational inertia times angular velocity. If an object has a large angular momentum, it's hard to stop spinning.

Torque

- Torque is a measure of how much a force acting on an object causes that object to rotate.

- Essential for spinning, torque is very important in ballet because a torque determines balance.

- If your torque is greater than zero, then you’re angular momentum may change, causing you to fall over

What is balance?

- No total torque and no total force. No total force is needed so that momentum does not change.

- No total torque is required so that the angular momentum does not change.

Centre of gravity

- The centre of gravity of an object is that point at which the object will balance.

- The entire weight may be considered as concentrated at this point, hence the name.

- In order to stay balanced, the centre of gravity must remain directly above the area of contact with the floor.

- If the area is very small, it will be harder to balance. For example, a dancer on pointe.

How can a dancer keep in balance while dancing?

- What’s the trick that keeps the dancer balanced when they are turning?

- The rotation axis should not wobble around too much.

The relevant quantities of turns are

-  Angular velocity is how fast an object spins

-  Rotational inertia is the inertia of a rotating object

-  Angular momentum is rotational inertia times angular velocity

-  A change in angular momentum is equal to torque exerted on an object times the duration the torque was acting on.

Force

• When a dancer’s force is pushing upward from the floor to the foot,  it is acting on the same vertical line as the force of gravity pulling downwards and the force of friction pulling outward, it uses Newton's 3rd Law of Motion- "For every action, there is always an equal and opposite reaction."

Perriouete

• Pirouettes are a rotation where the dancer supports themself with one leg, while the other leg is in retire position.

How pirouettes are made

• A pirouette is made by having a preparation followed by a rotational force, or torque, exerted against the floor. the torque on the floor against the dancer causes angular acceleration.
• fifth position has a small distance between the feet, thus a larger amount of force is required to do a pirouette, while fourth position has a larger amount of space between the feet, so it requires less force to produce the same turn.

Arabesque

• The supported leg is vertical and the other is extended behind the ballerina. An arabesque has more inertia than retire position.

Plie

• To apply vertical force in an upward direction, out of the ground, a dancer bends her knees in a position called plie.

Grand Jete is an example of projectile motion

• A grand jete is an example of a jump combined with projectile motion (meaning it’s a travelling leap). It begins with an initial velocity which will decrease as the dancer rises into the air until it (the velocity) reaches zero. Zero velocity is the maximum height.

Friction

• Friction is the force that keeps us standing without slipping. Friction is a horizontal force pulling across the floor, while gravity pulls down into the floor and the dancers foot is pulling upward out of the floor. If your foot is stationary on the ground, a large horizontal frictional force is possible, but when the foot is moving, the potential force is much smaller. Friction is a ballerina's best friend.

The concept of jumps and leaps

• Accelerations and forces are a part of all jumps
• Gravity acts vertically downward on the body of mass (our body)
• You only remain motionless if there is a vertical supporting force to your weight
• To jump off the ground, the dancer has to exert a (downward) force greater than her weight.
• The height of a jump is based on the downward vertical distance where the force is put off.

Why are dancers hair in a bun?

•  While spinning, dancers use the technique of spotting to keep them in a strait line. An object in motion tends to stay in motion unless acted on by an unbalanced force. Dancers keep their hair in a bun because otherwise, while spinning, their hair whipping around their head acts as an unbalanced force.

Experiment/research plans 

Why do you spin slower when your arms are out then when they are in front of you? 
Would you spin faster with your arms out on lino or in on carpet, and which if these options would make you fall over first? 
How do dancers not get dizzy? 

How do dancers not get dizzy 
While spinning, a dancer uses the technique of spotting to keep them in a straight line. They find a spot on the wall to look at to make sure they do not get dizzy. The goal of spotting is to maintain constant orientation of the dancers head and eyes, to the possible extent. They do this is in order to prevent dizziness and enhance control. As the dancers turn, spotting is performed by turning the head and body at different rates. When the body rotates smoothly at a constant speed, the head moves much faster and then stops. The dancer will fix their eyes on a particular spot.  

Why do you spin slower when your arms are out then when they are in front of you?
When a dancer draws their arms and legs and a leg inward, they reduce the between the axis of rotation and some of their mass. This reduces their moment of inertia. Since the angular momentum is conserved, her rotational velocity must increase to be decreased. To put it simply, the total amount of things that are spinning in preserved. The further out something is in the spin, the more it continues to the angular momentum for it's speed. Hence when you bring your arms towards the centre, you spin faster.