In some instances, when we consider a series of rigid bodies linked to each other, a physically meaningful quantity is the time rate of change of the angle between adjoining links. After all, muscles act on a joint to affect the angle between the articulating bones. The time rate of change of angle between adjoining body segments, when multiplied by the unit vector perpendicular to the plane of motion, is the angular velocity of one link relative to another in a multibody system. The angular velocity of body B (say the lower arm) with respect to body D (say the upper arm) is denoted by the symbol wB/D. Take a straight line fixed in D and another fixed in B as shown in Fig. 4.5. Let ^B/D be the angle taken in counterclockwise direction from the straight line fixed in D to the straight line fixed in B; then mb/d is given by the following equation:
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.