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Angular Momentum and Stability

Angular Momentum and Stability. While free in the air an object is not stable about its intermediate axis. Biom. 1. 2. 3. McGinnis. Axis 1: I max. Axis 2: I int. Axis 3: I min. r3. r3. r2. r1. r1. McGinnis. r2. Biomechanics.

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Angular Momentum and Stability

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  1. Angular Momentum and Stability While free in the air an object is not stable about its intermediate axis Dr. Sasho MacKenzie - HK 376

  2. Biom 1 2 3 McGinnis Axis 1: Imax Axis 2: Iint Axis 3: Imin r3 r3 r2 r1 r1 McGinnis r2 Biomechanics Applying the axis with the greatest radius of gyration (k) will have the greatest moment of inertia because the mass of the book doesn’t change. Moments of Inertia about 3 Axes of a Book Dr. Sasho MacKenzie - HK 376

  3. Maximum Moment of Inertia Axis (Imax) Axis that has the largest moment of inertia STABLE Minimum Moment of Inertia Axis (Imin) Axis that has the smallest moment of inertia Intermediate Moment of Inertia Axis (Iint) Has an intermediate moment of inertia. Determined not by its moment of inertia value, but rather because it is perpendicular to the both Imax and Imin. NOT STABLE Principle Axes Stability Dr. Sasho MacKenzie - HK 376

  4. Direction of torque and I t t t t 1 Iint 2 3 4 Book is Not Stable about Iint during rotation in the air This sequence is difficult to replicate in reality. It requires the precise application of a net force that only produces torque about Iint. Dr. Sasho MacKenzie - HK 376

  5. Direction of torque and I Top t 1 Iint 2 3 Other side of Book Top Other side of Book 4 Rotation about Iint will almost always include twist about Imin The book is still completing a full somersault but is also undergoing ½ twist during this time Dr. Sasho MacKenzie - HK 376

  6. Aerial Somersaults • When a gymnast, diver, or skier is performing an aerial somersault (rotation about the transverse axis) attempts must be made to prevent the inevitable twisting about the longitudinal axis. • This twisting occurs because rotation about the intermediate axis of the athlete is not stable. • There are two common methods that can be used to prevent twist. Dr. Sasho MacKenzie - HK 376

  7. Angular Momentum Twists • While somersaulting, it was shown during a recent lecture that rotating the limbs about the frontal (cartwheel) axis will introduce twist into the system. • Since twisting usually occurs while somersaulting, due to the instability of the intermediate axis, these rotations about the frontal axis will serve to prevent twist. Dr. Sasho MacKenzie - HK 376

  8. ITotal ITotal Somersault Axis Somersault Axis Angular Momentum Twists Twisting occurs when the somersault axis of the body is not in line with the angular momentum vector that was initially only producing a somersault rotation. No Twist, Only Somersault because somersault axis is parallel with ITotal Twisting and Somersault rotation because somersault axis not parallel with ITotal Dr. Sasho MacKenzie - HK 376

  9. ITotal ITotal Somersault Axis Angular Momentum Twists If the somersault axis is no longer in line with the angular momentum vector, then small rotations of the arms about the frontal axis can realign them. The instability of the intermediate axis (twisting occurs easily) also means that it requires only small rotations of the arms to prevent the twist. Dr. Sasho MacKenzie - HK 376

  10. Frontal Axis Frontal Axis Transverse Axis Transverse Axis Frontal : Imax Frontal : Iint Transverse : Iint Transverse : Imax Interchange Imax and Iint A second method that can be used to prevent twist while somersaulting in the air is to adjust position so that the somersault axis becomes Imax, and the frontal (cartwheel) axis becomes Iint. This can be accomplished by piking (or arching) at the hips and changing the relative trunk angle from 180 to approximately 135. Dr. Sasho MacKenzie - HK 376

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