Biomedical Engineering Reference
In-Depth Information
Fig. 4.3
(
a
) Disc of
radius
R
and mass
M
rotating about the
y
-axis.
(
b
) Representation of the
same situation with the
radius of gyration. Here, all
the mass
M
of disc (
gray
small sphere
)is
concentrated at the distance
k
of the axis of rotation
y
y
R
M
M
k
a
b
Fig. 4.4
(
a
) Disc of
radius
R
and mass
M
rotating about the
x
-axis.
(
b
) Representation of the
same situation with the
radius of gyration
R
M
x
x
k
M
a
b
of inertia that depends on the mass distribution about an axis has increased.
For a disc of radius
R
0.02 kg m
2
,
¼
0.20 m and
M
¼
1 kg, we obtain
I
x
¼
i.e., double that of
I
y
.
(c) Figure
4.5
shows a solid sphere of radius
R
and mass
M
that rotates about
any axis passing through its center of gravity. The moment of inertia in this
case will be the same, independent of the axis of rotation, due to the spherical
symmetry:
M
2
R
2
5
Mk
2
I
¼
¼
q
R
in this case
k
63
R
. A sphere can represent a crouched person,
clasping the knees during a revolution after a jump from a springboard. For a
sphere with
R
¼
:
0
0.016 kg m
2
.
¼
0.20 m and
M
¼
1 kg, we obtain
I
¼
