TRANSFER OF ANGULAR MOMENTUM IN THE

Tomohisa Miyanishi and Masakata Mukai Faculty of Physical Education, Sendai College, Miyagi 989-1693, Japan. ([email protected])

INTRODUCTION and HZ values because little angular momentum was needed in that direction. Therefore, in this discussion, we In a high speed pitching motion, one of the most important will concentrate on the changes in the HX and HZ values. 2 factors should be to obtain a large amount of angular At TSP the system had a CCW HX of 10 kg·m /s. This value 2 momentum from the ground, and then transfer as much of it changed to a CW HX of 13 kg·m /s at PSF. Since the GRF as possible to the throwing arm. Angular momentum for the in the YZ plane pointed upward and forward during the SS combined thrower-plus-ball system can be separated into (Miyanishi et al, 2001), the change of the HX was produced two parts, associated respectively with the motions of the by the vertical GRF. For the same reason, the change from 2 2 body-minus-throwing arm (“body-minus-arm”) and of the a CW HZ of 6 kg·m /s at TSF to a CCW HZ of 15 kg·m /s at throwing arm-plus-ball (“arm-plus-ball”) subsystems PSF was generated by the forward GRF during the SS2. (LeBlanc and Dapena, 1996). The purpose of this study was to clarify the changes in the At TSF, most of the system HX was in the body-minus-arm, angular momentum for the system during the fastball and most of the changes produced in HX during SS by the baseball pitch, and the transmission of angular momentum GRF also went into the body-minus-arm. During the 1st to the arm-plus-ball system. half of DS there was a gain of CW HX, all of which was transmitted from the ground through the legs and trunk to METHODS the throwing arm. During the 2nd half of DS there was no net gain of CW HX, but there was a transfer from the After the take-off of the stride leg (TSF), a right-handed body-minus-arm to the arm-plus-ball. At TSF, all the HZ elevates the left (stride) leg and turns the trunk of the system was in the body-minus-arm, and most of the toward the right, releases the ball from the glove (GRB), changes produced in the CCW HZ during the SS by the steps forward, plants the left foot (PSF), and releases the GRF also went into the body-minus-arm. During the 1st ball (BRL). The pitcher is in -support (SS) phase half of DS there was a gain of HZ, all of which was between TSF and PSF, and in double-support (DS) phase transmitted from the ground through the legs and trunk to between PSF and BRL. Fastball pitches made from level the throwing arm. During the 2nd half of DS there was no ground by five right-handed male varsity were net gain of HZ, but there was a transfer from the videotaped using three-dimensional (3D) DLT procedures. body-minus-arm to the arm-plus-ball. The 3D coordinate data of the 21 body landmarks and the Table 1. Angular momentum (kg·m2/s). (Mean±SD) ball centre were obtained for the fastest pitch of each subject, and smoothed using quintic spline as selected by Times: 1 2 3 4 5 6 7 the optimal cutoff frequencies for each coordinate. The TS GRB PSF BRL coordinates were expressed in an orthogonal reference HX F frame: The X axis pointed toward the right (normal to the body-minus-arm 1±2 1±1 3±2 -11±6 -11±5 -1±2 direction of the throw), the Y axis forward, and the Z axis arm-plus-ball 9±2 0±0 1±0 -1±1 -2±1 -7±4 -17±8 upward. The location of the center of mass and the angular system 1±0 1±2 2±1 3±4 -13±7 -18±8 -18±10 momentum values of 16 body segments and of the ball HY 10±2 were calculated using a method based on Dapena (1997). body-minus-arm -3±3 4±2 3±3 -7±4 -10±4 -5±4 The SS was divided into two phases (respectively SS1 and arm-plus-ball -4±4 0±0 1±0 1±1 3±1 7±1 -1±1 system 0±1 -2±3 5±3 4±4 -4±5 -3±4 -6±4 SS2) based on the instant of the GRB. The SS1, SS2 and HZ -4±4 DS phases were each divided into two equal time periods. body-minus-arm -1±0 2±2 8±2 13±2 13±1 8±1 The 3D angular momentum of the body-minus-arm, arm-plus-ball -5±2 0±0 0±0 -1±0 2±1 7±1 12±2 arm-plus-ball and combined system were calculated for system 0±0 -1±0 2±2 7±2 15±1 20±1 20±2 seven instants: (1) TSF, (2) the mid-point of SS1, (3) GRB, -6±2 (4) the mid-point of SS2, (5) PSF, (6) the mid-point of DS, and (7) BRL. REFERENCES RESULTS AND DISCUSSION Dapena, J. (1997). J. Applied Biomechanics, 13, 239-253. Average angular momentum values for the five pitches are LeBlanc, M.K., Dapena, J. (1996). Proceedings of XXth shown in Table 1. To facilitate the following discussion, the ASB, 157-158. terms “clockwise” (CW) and “counterclockwise” (CCW) Miyanishi, T., Mukai, M. (2001). Proceedings of XIXth will replace the signs of the X, Y and Z angular momentum ISBS, 108-111. components; the directions will correspond to views from the right, from behind and from overhead for the HX, HY and HZ angular momentum components, respectively. The changes of the system angular momentums depend on the angular impulses of the ground reaction forces (GRFs) received by the pitcher’s feet. The changes in the system HY values were much smaller than those of the system HX