PROBLEM 9.180
For the component described in Problem 9.165, 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 9.180 (Continued)
Using Eq. (9.57): 222
222
( ) [0.05984]( ) ] ( ) 1
xxz
or 2
( ) 0.998214
x
and 2
( ) 0.059740
y
22 2
( ) 3.4 ( ) 86.6 ( ) 90.0
xy z
K3: Begin with Eqs. (9.54b) and (9.54c) with 0.
yz zx
II
333
33
() ( )() 0
()()0
xy x y y
zz
IIK
IK
(ii)
PROBLEM 9.180 (Continued)
PROBLEM 9.181*
For the component described in Problems 9.145 and 9.149,
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 9.181* (Continued)
222
xyz
PROBLEM 9.181* (Continued)
PROBLEM 9.181* (Continued)
PROBLEM 9.182*
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.
PROBLEM 9.182* (Continued)
PROBLEM 9.182* (Continued)