Introduction to Sports Biomechanics: Analysing Human Movement ...

CAUSES OF MOVEMENT – FORCES AND TORQUES
approach may seem to be somewhat limited in sport, in which the net, or resultant,
effect of the forces acting is usually to cause the performer or object to accelerate, as in
Figure 5.10(a). In this figure, the resultant force can be obtained by moving the ground
reaction force, F, along its line of action, which passes through the centre of mass in this
case, giving Figure 5.10(b). As the resultant force passes through the runner’s centre of
mass, the runner can be represented as a point, the centre of mass, at which the entire
runner’s mass is considered to be concentrated: only changes in linear motion will occur
for such a force system. The resultant of F and G will be the net force acting on the
runner. This net force equals the mass of the runner, m, multiplied by the acceleration,
a, of the centre of mass. Symbolically, this is written as F + G = m a. This is one form of
Newton’s second law of motion (see Box 5.2).
More generally, as in Figure 5.10(c), the resultant force will not act through the
centre of mass; a torque – also called a moment of force – will then tend to cause the
runner to rotate about his or her centre of mass. The magnitude of this torque about a
point – here the centre of mass – is the product of the force and its moment arm, which
is the perpendicular distance of the line of action of the force from that point. Rotation
will be considered in detail later in this chapter.
It is possible to treat dynamic systems of forces, such as those represented in
Figure 5.10, using the equations of static equilibrium. To do this, however, we need to
introduce an imaginary force into the dynamic system, which is equal in magnitude
to the resultant force but opposite in direction, to produce a quasi-static force system.
Figure 5.10 Forces on a runner: (a) free body diagram of dynamic force system; (b) resultant force; (c) free body diagram with
force not through centre of mass.
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