Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
upper body, although this is not apparent because of the extremely high moment of inertia of the
earth. If the tennis player played the same shot with his feet off the ground, there would be a
torque on his lower body causing it to rotate counter to the movement of the upper body,
lessening the angular momentum in the arm–racket system.
Minimising inertia
The law of momentum (Box 5.3) allows derivation of the principle of minimising
inertia. The increase in angular velocity and, therefore, the reduction in the time taken
to move through a specified angle, will be greater if the moment of inertia of the whole
chain of body segments about the axis of rotation is minimised. Hence, for example,
in running – and particularly in sprinting – the knee of the recovery leg is flexed to
minimise the duration of the leg recovery phase.
Angular momentum of a rigid body
For a rigid body rotating about either an axis fixed in space, as in Figure 5.15(a), or a
principal axis of inertia, it can then be shown that, for planar motion, the angular
momentum (L) is the product of the body’s moment of inertia about the axis (I) and its
angular velocity (ω): that is, L = I ω. The direction of the angular momentum vector L,
Figure 5.15 Angular momentum: (a) single rigid body; (b) part of a system of rigid bodies.
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