Introduction to Sports Biomechanics: Analysing Human Movement ...

which is the same as that of ω, is given by allowing the position vector r to rotate
towards the velocity vector v through the right angle indicated in Figure 5.15(a). By
the right-hand rule, the angular momentum vector is into the plane of the page. The
SI unit of angular momentum is kg m 2 /s.
Angular momentum of a system of rigid bodies
For planar rotations of systems of rigid bodies, for example the sports performer, each
rigid body can be considered to rotate about its centre of mass (G), with an angular
velocity ω 2. This centre of mass rotates about the centre of mass of the whole system
(O), with an angular velocity ω 1, as for the bat of Figure 5.15(b). The derivation will
not be provided here, but the result is that the magnitude of the angular momentum
of the bat is: L = m r 2 ω 1 + I g ω 2. The first term, owing to the motion of the body’s
centre of mass about the system’s centre of mass, is known as the ‘remote’ angular
momentum. The latter, owing to the rigid body’s rotation about its own centre of mass,
is the ‘local’ angular momentum. For an interconnected system of rigid body segments,
representing the sports performer, the total angular momentum is the sum of the
angular momentums of each of the segments calculated as in the above equation. The
ways in which angular momentum is transferred between body segments can then be
studied for sports activities such as airborne manoeuvres in gymnastics or the flight
phase of the long jump.
GENERATION AND CONTROL OF ANGULAR MOMENTUM
Force couple
CAUSES OF MOVEMENT – FORCES AND TORQUES
A net external torque is needed to alter the angular momentum of a sports performer.
Traditionally in sports biomechanics, three mechanisms of inducing rotation, or
generating angular momentum, have been identified, although they are, in fact, related.
A force couple consists of a parallel force system of two equal and opposite forces (F)
which are a certain distance apart (Figure 5.16(a)). The net translational effect of these
two forces is zero and they cause only rotation. The net torque of the force couple is:
M = 2r × F. The × sign in this equation tells us that the position vector, r, and the force
vector, v, are multiplied vectorially (see Appendix 4.2). The resulting torque vector has
a direction perpendicular to, and into, the plane of this page. Its magnitude (2 r F) is the
magnitude of one of the forces (F) multiplied by the perpendicular distance between
them (2r).
The torque can be represented as in Figure 5.16(b) and has the same effect about a
particular axis of rotation wherever it is applied along the body. In the absence of an
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