PROBLEM B.71* (Continued)
333
xyz
PROBLEM B.72*
For the component described in Problem 9.167, determine (a) the
principal mass moments of inertia at the origin, (b) the principal axes of
inertia at the origin. Sketch the body and show the orientation of the
principal axes of inertia relative to the x, y, and z axes.
K
K
31.115W
g
PROBLEM B.72* (Continued)
(b) To determine the direction cosines , ,
x
yz
of each principal axis, use two of the equations of
y
222 2
() ( )() () 0
xy x y y yz z
IIkI
PROBLEM B.72* (Continued)
PROBLEM B.72* (Continued)
Adding and solving for
3
()
z
333
xyz
PROBLEM B.73*
For the component described in Problem 9.168, determine (a) the
principal mass moments of inertia at the origin, (b) the principal
axes of inertia at the origin. Sketch the body and show the
orientation of the principal axes of inertia relative to the x, y, and z
axes.
SOLUTION
(a) From the solution to Problem 9.168, we have
I
I
g
I
I
4
4
18.91335
x
t
I
a
g
t
4
4
1.33333
xy
t
I
a
g
t
PROBLEM B.73* (Continued)
319.08 t
g
(b) To determine the direction cosines , ,
x
yz
of each principal axis, use two of the equations of
Eq. (9.54) and Eq. (9.57). Then
xyz
PROBLEM B.73* (Continued)
2:K Begin with Eqs. (9.54a) and (9.54b):
()()()()0
xxxyyzxz
IK I I
22 2
0.13913( ) ( ) 0.74522( ) 0
xy z
Adding and solving for 2
()
z
PROBLEM B.73* (Continued)
Simplifying
333
xyz
PROBLEM B.74*
For the component described in Problems 9.148 and 9.170,
determine (a) the principal mass moments of inertia at the origin,
(b) the principal axes of inertia at the origin. Sketch the body and
show the orientation of the principal axes of inertia relative to the
x, y, and z axes.
SOLUTION
PROBLEM B.74* (Continued)
xyz
PROBLEM B.74* (Continued)
3
x
33
yz