Fundamentals of Biomechanics

Figure 5.9. The optimal projection angles for most basketball
jump shots are between 49 and 55° above the
horizontal (hatched). These initial trajectories represent
the right mix of low ball speed and a good angle
of entry into the hoop. Novice shooters (N) often
choose a low angle of release. Skilled shooters (S) really
do not shoot with high arcs, but with initial trajectories
that are in the optimal range and tailored to the
conditions of the particular shot.
desirable initial angles of projection. These
general rules are likely to be effective for
most performers. Care must be taken in applying
these principles in special populations.
The biomechanical characteristics of
elite (international caliber) athletes or
wheelchair athletes are likely to affect the
optimal angle of projection. Kinesiology
professionals should be aware that biomechanical
and environmental factors interact
to affect the optimal angle of projection. For
example, a stronger athlete might use an
angle of release slightly lower than expected
but which is close to optimal for her. Her
extra strength allows her to release the implement
at a higher point without losing
projectile speed so that she is able to use a
CHAPTER 5: LINEAR AND ANGULAR KINEMATICS 121
slightly lower angle of release. Professionals
coaching projectile sports must keep
up on the biomechanical research related to
optimal conditions for their athletes.
ANGULAR MOTION
Angular kinematics is the description of
angular motion. Angular kinematics is particularly
appropriate for the study of human
movement because the motion of most
human joints can be described using one,
two, or three rotations. Angular kinematics
should also be easy for biomechanics students
because for every linear kinematic
variable there is a corresponding angular
kinematic variable. It will even be easy to
distinguish angular from linear kinematics
because the adjective “angular” or a Greek
letter symbol is used instead of the Arabic
letters used for linear kinematics.
Angular displacement (: theta) is the
vector quantity representing the change in
angular position of an object. Angular displacements
are measured in degrees, radians
(dimensionless unit equal to 57.3º), and
revolutions (360º). The usual convention to
keep directions straight and be consistent
with our 2D linear kinematic calculations is
to consider counterclockwise rotations as
positive. Angular displacement measured
with a goniometer is one way to measure
static flexibility. As in linear kinematics,
the frames of reference for these angular
measurements are different. Some tests define
complete joint extension as 0º while
other test refer to that position as 180º. For
a review of several physical therapy static
flexibility tests, see Norkin & White (1995).
In analyzing the curl-up exercise
shown in Figure 5.10, the angle between
the thoracic spine and the floor is often
used. This exercise is usually limited to the
first 30 to 40º above the horizontal to limit
the involvement of the hip flexors
(Knudson, 1999a). The angular displacement
of the thoracic spine in the eccen-