The Physics of dance

•Introduction

•Balance

•The physic of turn

• Jumps (and black holes...)

• Why are dancers so sli m?

The physics behind the body size!

Content

Introduction

Some Physics vocabulary •Angular velocity (ω): how fast something spins and in what direction its rotation axis points.

•Angular momentum (L) : The magnitude of an object’s angular

momentum gives an indication of how hard it is to bring to a stop.

More Physics Vocabulary• Centrifugal force : Effective f

orce pushing something to the outsid e of a turn.

Still More Physics Vocabulary

Torque ( ): “off center” forces which

can cause something to spin.

About torque...Torque changes angular momentum:

• The harder you push, the more quickly the object “spins up.”

• The further from the spin axis you applythe forces, the more quickly the objectspins up.

• The longer you push, the greater thetotal change in angular momentum.

• If no torque is applied to a rigid object,its spin axis doesn't wobble.

The Physics of balance

Centre of Gravity• The center of gravity is a geometric

property of any object . The center of gravity is the average location of the weight of an object.

• The center of mass of a system of particles is defined as the average of their positions, weighted by their masses, mi:

Point C is the centre of Mass

Forces on a Balanced Dancer• Gravity (pulls down, acts at c.g.) + supp

ort from floor (pushes up, acts at feet)

• Forces sum to zero; both forces “ point through” the dancer's center of gravity, so

torque is zero.

An example

• Forces on each dancer sum to zero. Though some forces are “off-center” torques also sum to zero.

Staying Balanced

Staying balanced: center of gravity remains directly above the area of contact with the floor. Otherwise τ ! ≠ 0 : you’d tip over.

Static Balance

• Net force is zero (otherwise your momentum

would change: you might fall)• Net torque is zero (otherwise your angular

momentum would change: you might tipover)

The Physics of turns

What describes turn ? The relevant quantities that describe turns are:

• Angular velocity is how fast an object spins• Rotational inertia is the inertia of a rotating obje

ct• Angular momentum is rotational inertia times an

gularvelocity

• A change in angular momentum is equal to the torque

exerted on an object times the duration of time the torque was acting

What stands for ‘What’

• is angular momentum• is rotational inertia• is angular velocity• is torque

The Physics of Turns• indicates how hard it is to start something

spinning (just as mass is an indication of how hard it is to start something moving).

if no torque is applied must beconstant.

• Decreasing will increase• Increasing will decrease

Relationship between and spin rate

Increasing decreases Spin rate

Increasing decreases Spin rate

The Physic

s of

jumps

The Physics of jumps

• Gravitational for ce plays a major ro

le in jumps

• The total effect o f gravity is the sam e as if it were actin g on the dancer's c

enter of gravity only

• Gravity only affe cts vertical (not h

orizontal) motion

• Gravitational for ce is proportional to an object's mas

s

Horizontal VS Vertical motion

Trajectory in a jump

Floating

Body size effects

A dancer’s body evolution

Pierina Legnani - (1 8 6 3 1 9

2 3 )

Sylvie Guillem Royal Ballet Principal

Never exaggerate

Conclusion