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 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