This equation is called the principle of superposition of angular velocity. We illustrate its use by considering the relative angular velocities of various body segments during vertical jumping.
Example 4.2. Body Segment Motions During Jumping. In Example 4.1 we found the following values for the angular velocities of the foot (f), leg (l), thigh (t), and trunk (c) at 0.2 s after the beginning of the prepatory phase of the vertical jumping:
Using Eqn. 4.19, we can show that the angular velocity of the leg with respect to the foot is given by the following equation:
This result indicates that the angle between the leg and the foot at the ankle is increasing at t = 0.2 s. This rate of rotation is principally caused by the contraction of the calf muscle.
Figure 4.5. Relative rotation of rigid object B with respect to another rigid object D in planar motion parallel to the (ej, e2) plane. The angle ^B/D is drawn counterclockwise from a straight line fixed in D to another straight line that rotates with B. Both lines are parallel to the (e1, e2) plane.
Let us next compute the angular velocity of the thigh with respect to the leg:
This value corresponds to the extension of the leg, and the primary muscle group that actuates leg extension are the quads.
The angular velocity of the trunk relative to the thighs is given by the following equation:
This equation points to extension at the hip joint, which is the primary action of the hamstrings. Thus, at the instant of vertical jumping, calf muscles, quads, and hamstrings appear as actuators of relative motion of various body segments. Antagonists to these muscle groups are also activated to bring accuracy and control to the movement. Bobbert and van Ingen Schenau (1988) found that the sequence that is realized by the pattern of muscle activation is upper body, upper legs, lower legs, and feet.
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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.