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PROBLEM B.25
A 2-mm thick piece of sheet steel is cut and bent into the machine
component shown. Knowing that the density of steel is 7850 kg/m3,
determine the mass moment of inertia of the component with
respect to each of the coordinate axes.
SOLUTION
z
PROBLEM B.25 (Continued)
z
PROBLEM B.26
A 2-mm thick piece of sheet steel is cut and bent into the
machine component shown. Knowing that the density of steel is
7850 kg/m
3
, determine the mass moment of inertia of the
component with respect to each of the coordinate axes.
SOLUTION
x
PROBLEM B.26 (Continued)
z
PROBLEM B.27
A subassembly for a model airplane is fabricated from three pieces of 1.5-
mm plywood. Neglecting the mass of the adhesive used to assemble the
three pieces, determine the mass moment of inertia of the subassembly
with respect to each of the coordinate axes. (The density of the plywood
is
3
780 kg/m .)
SOLUTION
x
PROBLEM B.27 (Continued)
z
PROBLEM B.28
A section of sheet steel 0.03 in. thick is cut and bent into the
sheet metal machine component shown. Determine the mass
moment of inertia of the component with respect to each of the
coordinate axes. (The specific weight of steel is 490 lb/ft3.)
SOLUTION
18
v
For composite area:
PROBLEM B.28 (Continued)
Plate 2 in x-z plane:
Note: By Eqn. 9.38,
y
z
z
PROBLEM B.29
A framing anchor is formed of 0.05-in.-thick galvanized steel. Determine the
mass moment of inertia of the anchor with respect to each of the coordinate
axes. (The specific weight of galvanized steel is
3
470 lb/ft .)
SOLUTION
62
2006.14 10 lb s /ft
Using Figure 9.28 for components 1 and 2 and the equations derived above for component 3, we have
123
62 2
() () ()
1(3325.97 10 lb s /ft)(3.5 in.)
xx x x
II I I
PROBLEM B.29 (Continued)
62 2 22
1(2006.14 10 lb s /ft)[(4.75) (2) ] in
18
y
PROBLEM B.29 (Continued)
123
62 2 22
() () ()
1(3325.97 10 lb s /ft)[(2.25) (3.5) ] in
zz z z
II I I
z
PROBLEM B.30*
A farmer constructs a trough by welding a rectangular piece
of 2-mm-thick sheet steel to half of a steel drum. Knowing
that the density of steel is
3
7850 kg/m
and that the thickness
of the walls of the drum is 1.8 mm, determine the mass
moment of inertia of the trough with respect to each of the
coordinate axes. Neglect the mass of the welds.
SOLUTION
34
2
1.80282 kg
Using Figure 9.28 for component 1 and the equations derived above for components 2 through 4, we have
34
() ()
xx
II
x
PROBLEM B.30* (Continued)
1234
222
() () () ()
1(2.76948 kg)[(0.84) (0.21) ] m
yy y y y
II I I I
y
1234
() () () ()
zz z z z
II I I I
1(1.80282 kg)(0.285 m)
z
PROBLEM B.31
The machine element shown is fabricated from steel.
Determine the mass moment of inertia of the assembly with
respect to (a) the x axis, (b) the y axis, (c) the z axis. (The
density of steel is
3
7850 kg/m .)
SOLUTION
First compute the mass of each component. We have
ST
mV
3
Using Figure 9.28 and the parallel-axis theorem, we have
x
PROBLEM B.31 (Continued)
(b) 123
() () ()
yy y y
II I I
[(20.20269) (0.11838 0.94701)
y
(c) 123
() () ()
zz z z
II I I
1(0.59188 kg)[3(0.02) (0.06) ] m (0.59188 kg)[(0.04) (0.03) ] m
z
To the Instructor:
The following formulas for the mass of inertia of a semicylinder are derived at this time for use in the
solutions of Problems 9.142 through 9.145.
PROBLEM B.32
Determine the mass moments of inertia and the radii of
gyration of the steel machine element shown with respect
to the x and y axes. (The density of steel is 7850 kg/m
3
.)
SOLUTION
x
PROBLEM B.32 (Continued)
y
PROBLEM B.33
Determine the mass moment of inertia of the steel machine
element shown with respect to the x axis. (The density of
steel is
3
490 lb/ft .)
SOLUTION
2"
12 12 12 12
x
PROBLEM B.33 (Continued)
Half-cylinder about base,
2" 2'
2
2
53
0.7639
xx
IImd
x
