1. 12/16/2015Dr. Sasho MacKenzie - HK 3761 Twisting Rotation about the longitudinal axis http://physics.weber.edu/galli/catflip/catflip.html

2. 12/16/2015 Dr. Sasho MacKenzie - HK 3762 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.

3. 12/16/2015 Dr. Sasho MacKenzie - HK 3763 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

4. 12/16/2015 Dr. Sasho MacKenzie - HK 3764 Cat Twist Technique 1. Layout position with back to floor Legs Trunk 2. Pike at the hips with back to floor About Axis A, I legs > I trunk Axis A 3. Muscular force creates a torque about Axis A and the trunk twists to face the ground. Axis A

5. 12/16/2015 Dr. Sasho MacKenzie - HK 3765 Cat Twist Technique 4. Muscular force creates a torque about Axis B and the legs twist to face the ground. About Axis B, I trunk > I legs 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 3 rd Law]

6. 12/16/2015 Dr. Sasho MacKenzie - HK 3766 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.

7. 12/16/2015 Dr. Sasho MacKenzie - HK 3767 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 I  Total = I 1  1 + I 2  2 = 0 Hips Body and top of turntable The same conditions apply for an athlete free in the air.

8. 12/16/2015 Dr. Sasho MacKenzie - HK 3768 Transverse Axis Longitudinal Axis 3 Principal Axes for a Human in Anatomical Position Frontal Axis Frontal = I max (Cartwheel) Transverse = I int (Back flip) Longitudinal = I min (Figure skating spin)

9. 12/16/2015 Dr. Sasho MacKenzie - HK 3769 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.

10. 12/16/2015 Dr. Sasho MacKenzie - HK 37610 Angular Momentum Twists Initial angular momentum = I  Total    t =  I  I  Total = I  initial +    t This means that if the arms rotate CCW, then the trunk must rotate CW.

11. 12/16/2015 Dr. Sasho MacKenzie - HK 37611 Angular Momentum Twists Twist Axis Somersault Axis Initial angular momentum = I  Total Twist Component Somersault Component I  Total

12. 12/16/2015 Dr. Sasho MacKenzie - HK 37612 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?