Biomedical Engineering Reference
In-Depth Information
Fig. 4.9
Principal axes of
rotation for a human body
that rotates freely, without
support
longitudinal
10.5-13.0 kg m
2
.
I
transverse of man crouched with the hands on the knees
¼
I
transverse of man standing with arms along the body
¼
4.0-5.0 kg m
2
.
I
anteroposterior of man standing with arms along the body
¼
12.0-15.0 kg m
2
.
Example 4.2
The moment of inertia of a person with 70 kg mass and 1.70 m height
about the longitudinal principal axis with the person's arms along the body is
I
1.0 kg m
2
as illustrated in Fig.
4.9
. (a) Determine the radius of gyration
about the longitudinal principal axis. (b) Suppose that an equivalent geometric
model to this person is a cylinder of 70 kg mass and 1.70 m height. Find the radius
of this cylinder.
Observe that the radius of gyration is the distance from the place where the total
mass of the body can be concentrated to produce the same moment of inertia for the
given axis of rotation.
(a) 1.0 kg m
2
¼
(70 kg)
k
2
; isolating
k
, we obtain
¼
s
1
:
0kgm
2
70 kg
k
¼
¼
0
:
12 m
:
q
2
I
M
MR
2
/2; hence,
R
(b) In this case
I
¼
¼
¼
0
:
17m
¼
17 cm . This model is
reasonable.
Exercise 4.2
A person with 70 kg has a radius of gyration equal to 0.17 m about the
main longitudinal axis when she or he is with outstretched arms at an angle of 90
in
