Introduction to Sports Biomechanics: Analysing Human Movement ...

The ways of obtaining body segment data, including masses and locations of centres
of mass, were briefly outlined in Chapter 4. The positions of the segmental end points
are obtained from some visual record, usually a video recording of the movement. For
the centre of mass to represent the system of segmental masses, the moment of mass
(similar to the moment of force) of the centre of mass must be identical to the sum of
the moments of body segment masses about any given axis. The calculation can
be expressed symbolically as: m r = Σm i r i, or r = Σ(m i /m)r i, where m i is the mass of
segment number i, m is the mass of the whole body (the sum of all of the individual
segment masses Σm i); (m i/m is the fractional mass ratio of segment number i; and r and
r i are the position vectors, respectively, of the centre of mass of the whole body and the
centre of mass of segment number i. In practice, the position vectors are specified by
their two-dimensional (x, y) or three-dimensional (x, y, z) coordinates. Table 5.1 (see
page 221) shows the calculation process for a two-dimensional case with given
segmental mass fractions and position of centre of mass data (see also Study task 3).
FUNDAMENTALS OF ANGULAR KINETICS
Almost all human motion in sport and exercise involves rotation (angular motion), for
example the movement of a body segment about its proximal joint. In Chapter 3, we
considered the kinematics of angular motion. In this section, our focus will be on the
kinetics of such motions.
Moments of inertia
CAUSES OF MOVEMENT – FORCES AND TORQUES
In linear motion, the reluctance of an object to move (its inertia) is expressed by its
mass. In angular motion, the reluctance of the object to rotate depends also on
the distribution of that mass about the axis of rotation, and is expressed by the moment
of inertia. The SI unit for moment of inertia is kilogram-metres 2 (kg m 2 ); moment of
inertia is a scalar quantity. An extended (straight) gymnast has a greater moment of
inertia than a piked or tucked gymnast and is, therefore, more ‘reluctant’ to rotate. This
makes it more difficult to somersault in an extended, or layout, position than in a piked
or tucked position. Formally stated, the moment of inertia is the measure of an object’s
resistance to accelerated angular motion about an axis. It is equal to the sum of the
products of the masses of the object’s elements and the squares of the distances of those
elements from the axis of rotation. Moments of inertia can be expressed in terms of the
radius of gyration, k, such that the moment of inertia (I) is the product of the mass (m)
and the square of the radius of gyration: I = m k 2 .
The moments of inertia for rotation about any point on a three-dimensional rigid
body are normally expressed about three mutually perpendicular axes of symmetry;
the moments of inertia about these axes are called the principal moments of inertia. For
the sports performer in the anatomical reference position, the three principal axes of
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