Biomedical Engineering Reference
In-Depth Information
Fig. 4.5
(
a
) Solid sphere of
radius
R
and mass
M
that
rotates about an axis
passing through its center.
(
b
) Representation of
the same situation with
the radius of gyration
R
M
M
k
a
b
Fig. 4.6
(
a
) Solid cylinder
with radius
R
and mass
M
that rotates about the
x-
axis. (
b
) Representation
of the same situation with
the radius of gyration
R
a
x
L
M
M
k
b
x
(d) Figure
4.6
shows a solid cylinder of radius
R
, length
L
, and mass
M
that
rotates about the
x
-axis passing through its center of gravity. The moment of
inertia is
2
M
R
2
Mk
2
I
x
¼
¼
in this case,
k
¼
0.71
R
. An upper arm or a forearm can be represented by a
cylinder. Note that in this case the moment of inertia does not depend on the
length
L
. For a cylinder of radius
R
¼
0.05 m,
L
¼
0.20 m, and
M
¼
1 kg,
0.0013 kg m
2
.
we obtain
I
x
¼
