Biomedical Engineering Reference
In-Depth Information
It is worthwhile to make a final observation related to the conservation of total
angular momentum in the absence of external torques. There are motions of legs,
arms, and hips that allow transference of rotation from a main axis to another axis.
This is observed during aerial evolutions in circus acrobatics, in ornamental jumps,
and in several Olympic gymnastics modalities where, during a jump with apparent
rotation about a main transverse axis, the athlete also presents a screw rotation.
In the case of total angular momentum equal to zero, its conservation requires
possible rotations which occur at least in two body segments, where one segment
balances the angular momentum of the other segment.
4.6 Variation of Angular Momentum
When an external nonzero resultant force acts on a body, producing an external
torque, the variation of the angular momentum occurs during the time interval
corresponding to the duration of action. The force of reaction from a surface is very
common in producing the angular impulse with which the rotation begins in aerial
trials. This situation is shown in Fig.
4.12
.
Example 4.5
Consider that the diver of Fig.
4.12
has a mass of 60 kg and a radius of
gyration
k
0.45 m about the main transverse axis. The force of reaction from the
springboard on the diver has a magnitude of 600 N and its lever arm
d
¼
0.15 m.
The force of reaction acts 0.5 s during the jump. Determine the angular momentum
introduced on the diver as well as the angular velocity with which the diver leaves the
springboard.
¼
F
R
C.G.
Fig. 4.12
Representation
of a diving jump in which
the force of reaction from
the springboard on the diver
is responsible for the
introduction of the angular
momentum which will be
conserved during the jump
d
