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The ballet barre also extends the base of support, with the hand acting as a “third foot.”

Base of

Support

Foot

Toe

Hand

Slide 28

Motion & Center of Gravity

2

3

4

5

7

3

1

5

1

6

7

A spinning object turns about its center of gravity as it flies through the air.

The center of gravity follows a parabolic trajectory which is the same for all objects.

Note: If axe is about 10” long then 4 frames between keys.

General tumbling motion (e.g., throw a chair) is very complicated!

Arbitrary

Slide 29

Movie: Grand Jeté

Slide 30

Jumps & Center of Gravity

While a dancer is in the air (not in contact with the floor) the only force on the dancer is gravity and the trajectory of the center of gravity is a parabolic arc.

During a two foot vertical jump a dancer is in the air for slightly less than ¾ of a second.

If the dancer’s horizontal speed is 10 feet per second then the CG travels about 7.1 feet during the jump.

CG

CG

If the dancer jumps a lesser height then the time in the air decreases

Slide 31

Shifting the Center of Gravity

By raising their arms and legs, dancers can raise the location of their center of gravity (CG).

CG

CG

Near hips

Lower torso

Slide 32

Grand Jeté Floating Illusion

Shifting the CG upward, the distance the dancer’s head rises is reduced, giving illusion of floating longer.

Time in the air is 25% longer than a similar leap where the CG rises only 1.3 feet

Slide 33

Grand Jeté Floating Illusion

Illusion of floating is enhance by the fact that during the peak of the jump the vertical motion is the slowest.

Slide 34

Newton’s Second Law of Motion

Acceleration occurs when an object’s velocity changes, such as speeding up or slowing down.

Acceleration depends on Force and Mass.

Acceleration is always in the direction of the net Force acting on an object.

(Acceleration) =

(Net Force)

(Mass)

Slide 35

Newton’s Second Law (Part 1)

The greater the force on acting on an object, the greater the acceleration of that object.

Slide 36