Rotations - Biomechanics of the Human Body - page 70

8 : 1kgm 2 = s

ω ¼

2 ¼

11 : 15 rad = s :

ð Þ ð : Þ

60 kg 0 11 m

If in 1 s she turns through an angle of 11.15 rad, in 30 s she will turn 334.5 rad.
As 1 turn ¼ 2 π rad ¼ 6.28 rad, the number of turns she will complete is 53.

Exercise 4.4 A diver with 65 kg is standing, facing the swimming pool. He puts his
arms behind him and at the moment of the jump receives an angular impulse of
reaction on his feet exerted by the springboard. The rotation of his arms also
introduces angular momentum in the process of jumping. His rotational motion
will occur about the main transverse axis. Knowing that when he leaves the
springboard, his radius of gyration is 0.5 m and his angular velocity is 3.5 rad/s,
determine the diver's angular velocity at the moment when he passes from the
outstretched posture to the curved, clasping his knees, decreasing his radius of
gyration to 0.28 m. Find the diver's angular momentum during the jump. The
greater the angular momentum reached, the larger is the number of turns in the
air that he can perform before touching the water's surface.

Another example of angular momentum conservation occurs during the spike in
a volleyball game. During a jump, the rotation of arms with large angular velocity
in the direction of the ball is necessarily accompanied by the leg's rotational motion
(in opposite direction). The legs, being heavier than the arms and, therefore, with
smaller angular velocity, their angular momentum compensates the arm's angular
momentum. Figure 4.11 illustrates this situation. The initial angular momentum is
zero and, hence, during the spike, must remain zero, which explains the reason for
compensation.

Fig. 4.11 Example of
angular momentum
conservation in a spike
in volleyball game.
The angular momentum
introduced by the rotation
of the arms is compensated
by the rotational motion
of legs