Rotations - Biomechanics of the Human Body - page 64

Fig. 4.7 ( a ) Solid cylinder
with radius R , length L ,
and mass M that rotates
about the y -axis passing
through the center of
gravity. ( b ) Representation
of the same situation with
the radius of gyration

y

R

a

M

L

b

M

k

(e) Figure 4.7 shows a solid cylinder of radius R , length L , and mass M that rotates
about the y -axis passing through its center of gravity. In this case,

M 3 R 2

L 2

þ

Mk 2 I y ¼ ¼

12

and k ¼ 0.50 R + 0.29 L . For a cylinder with R ¼ 0.05 m, L ¼ 0.20 m, and

0.004 kg m 2 . Note that changing the position of the
axis of rotation, the moment of inertia changed and now it depends on the
cylinder length. To rotate this same cylinder about the y -axis is 3.0 times more
difficult than about the x -axis, both passing through the center of gravity.
(f) Figure 4.8 shows a solid cylinder of radius R , length L , and mass M that rotates
about an axis passing through one of the bases. It is possible to obtain the
moment of inertia of a body, when the axis of rotation is parallel to an axis
passing through its center of gravity by applying the theorem of parallel axis.

M ¼ 1 kg, we obtain I y ¼

4.3.2 Parallel Axis Theorem

The moment of inertia of a body can be calculated in relation to any axis of
rotation previously defined. The moments of inertia in relation to the axis of
rotation passing through its center of gravity have great applications and are
calculated and tabulated. Observe that

the moments of inertia of bodies of