Biomechanical analysis of fundamental human movements by Arthur Chapman

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This is moment of inertia (henceforth represented by MI, symbol I or J), which is a measure of a combination of mass and distribution of the mass away from the CM. 6 Distribution of segmental masses determines the position of the whole-body CM. 7 Distribution of segmental masses changes not only the position of the CM, but also the magnitude of MI by a squared factor of the distribution. ment of the mass from the CM, and has the dimensions of ML2. 7 gives a diagrammatic meaning to MI. 7a shows how the square of the distribution of the mass contributes to the calculation of MI.

Conservation and Transfer of Energy At any instant when a muscle is producing force and shortening simultaneously, the integral of force with respect to shortening displacement is work. 2. 2a-c, the individual masses have oppositely directed velocities and momenta that sum to zero because of their vectorial nature, and the CM of the system does not change position. Despite no change in position of the system CM, total KE is conserved as the sum of the KE of the individual masses, since KE is a scalar quantity.

IA = IG + mr2 ¢ Key Point Distribution of segmental masses determines the MI about the wholebody CM, and the parallel axis theorem relates MI calculated about one axis to that calculated about a parallel axis. 14) In gymnastics activities, it is clear that the moment of inertia of the body is smaller during rotation about an axis through the CM than during rotation in an extended form about the horizontal bar. Angular Impulse–Angular Momentum Relationship The previous information on rotational inertia allows us to develop the rotational equivalents of the prior equations that apply to linear motion.

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