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PROBLEM 9.182* (Continued)
PROBLEM 9.183*
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.
PROBLEM 9.183* (Continued)
PROBLEM 9.183* (Continued)
PROBLEM 9.183* (Continued)
PROBLEM 9.184*
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.
1113
() () ( )() 0
zx x yz y z z
II IK
PROBLEM 9.184* (Continued)
PROBLEM 9.184* (Continued)
3333
() () ( )() 0
zx x yz y z z
II IK
Substituting
33
(0.096768)( ) (0.41933 0.51621)( ) 0
xy
33
(0.096768)( ) (0.41933 0.51621)( ) 0
xz
Simplifying yields
33 3
() () ()
yz x
Now substitute into Eq. (9.57):
22
33
() 2[()] 1
xx
(i)
or
3
1
() 3
x
and
3
1
() () 3
yz
333
( ) 54.7 ( ) ( ) 125.3
xyz
(c)
Note: Principal axis 3 has been labeled so that the principal axes form a right-handed set. To obtain
the direction cosines corresponding to the labeled axis, the negative root of Eq. (i) must be chosen;
That is,
3
1
() 3
x
Then
3
( ) 125.3
x
33
() () 54.7
yz
PROBLEM 9.185
Determine by direct integration the moments of inertia of the
shaded area with respect to the x and y axes.
PROBLEM 9.186
Determine the moment of inertia and the radius of gyration of the shaded
area shown with respect to the y axis.
