04/21/23 Dr. Sasho MacKenzie - HK 376 1

Twisting

Rotation about the longitudinal axis

http://physics.weber.edu/galli/catflip/catflip.html

04/21/23 Dr. Sasho MacKenzie - HK 376 2

Type 1: External Torque about the Longitudinal Axis

• An external force is applied to the athlete at a distance from their longitudinal axis.

• This creates a torque about the longitudinal axis which results in a change in angular momentum (twist).

• Commonly used for rotation from (0-180)• Basketball, hockey, and football defense.

04/21/23 Dr. Sasho MacKenzie - HK 376 3

Type 2: Zero Angular Momentum Twists

• The athlete is free in the air with zero angular momentum about all axes.

• The athlete performs a series of actions that can introduce twist and then remove twist from the body.

a) Cat Twist Technique

b) Counter-Rotational (Hula Hoop) Technique

04/21/23 Dr. Sasho MacKenzie - HK 376 4

Cat Twist Technique

1. Layout position with back to floor

Legs Trunk

2. Pike at the hips with back to floor

About Axis A, Ilegs > Itrunk

Axis A

3. Muscular force creates a torque about Axis A and the trunk twists to face the ground.

Axis A

04/21/23 Dr. Sasho MacKenzie - HK 376 5

Cat Twist Technique

4. Muscular force creates a torque about Axis B and the legs twist to face the ground.

About Axis B, Itrunk > Ilegs

Axis A

Axis B

3. The legs rotate in the opposite direction as the trunk, but not by as much due to their larger moment of inertia about Axis A. [Newton’s 3rd Law]

04/21/23 Dr. Sasho MacKenzie - HK 376 6

Cat Twist Technique

The athlete has successfully completed 180 of twist with a net angular momentum of zero.

The pike is the key element to this technique. It gives upper and lower body segments different moments of inertia about the same axis. This allows each segment to twist against the higher resistance (moment of inertia) of the other.

04/21/23 Dr. Sasho MacKenzie - HK 376 7

Counter-Rotational Technique

This type of twisting also does not require any initial angular momentum. This can be demonstrated on a turntable. Rotating the hips in one direction will result in the body twisting in the opposite direction in order to conserve angular momentum.

If, t = 0 then I = 0

ITotal = I11 + I22 = 0

Hips Body and top of turntable

The same conditions apply for an athlete free in the air.

04/21/23 Dr. Sasho MacKenzie - HK 376 8

Transverse Axis

Longitudinal Axis

3 Principal Axes for a Human in Anatomical Position

Frontal A

xis

Frontal = Imax

(Cartwheel)

Transverse = Iint

(Back flip)

Longitudinal = Imin

(Figure skating spin)

04/21/23 Dr. Sasho MacKenzie - HK 376 9

Type 3: Angular Momentum Twists

With angular momentum type twists, there is angular momentum put into the system about the transverse axis (somersault) before it begins to freely rotate.

Some of this angular momentum is then transferred to the longitudinal axis by applying internal muscular torques which results in changes of angular momentum to parts of the system.

04/21/23 Dr. Sasho MacKenzie - HK 376 10

Angular Momentum Twists

Initial angular momentum = ITotal

t = IITotal = Iinitial + t

This means that if the arms rotate CCW, then the trunk must rotate CW.

04/21/23 Dr. Sasho MacKenzie - HK 376 11

Angular Momentum Twists

Twist Axis

Somersault Axis

Initial angular momentum = ITotal

Twist Component

Somersault Component

ITotal

04/21/23 Dr. Sasho MacKenzie - HK 376 12

Final Exam Question

• You are viewing a diver from the opposite end of the pool. The diver is attempting a 1 and ½ backwards somersault with a half twist. From your perspective, at the end of the pool, the diver moves her left arm up and drops her right arm down. In which direction (cw or ccw) will the twist occur as viewed from the ceiling given the above scenario?