ANTHROPOMETRY - Biomechanics and Motor Control of Human Movement - page 89

Figure 4.4 Center of mass of a three-segment system relative to the centers of mass
of the individual segments.

4.1.5 Mass Moment of Inertia and Radius of Gyration
The location of the center of mass of each segment is needed for an analysis of
translational movement through space. If accelerations are involved, we need
to know the inertial resistance to such movements. In the linear sense, F ma

describes the relationship between a linear force F and the resultant linear
acceleration a . In the rotational sense, M

=

I α . M is the moment of force
causing the angular acceleration α . Thus, I is the constant of proportionality
that measures the ability of the segment to resist changes in angular velocity.
M

=

m 2 . The value of
I depends on the point about which the rotation is taking place and is a
minimum when the rotation takes place about its center of mass. Consider a
distributed mass segment as in Figure 4.3. The moment of inertia about the
left end is:

m, α is in rad / s 2 , and I has units of N · is in kg ·

m 1 x 1 + m 2 x 2 +···+ m n x n

I =

n

m i x i = (4.8)

i = 1

It can be seen that the mass close to the center of rotation has very little
influence on I , while the furthest mass has a considerable effect. This principle
is used in industry to regulate the speed of rotating machines: the mass of a
flywheel is concentrated at the perimeter of the wheel with as large a radius as
possible. Its large moment of inertia resists changes in velocity and, therefore,
tends to keep the machine speed constant.