1107
10–94.
SOLUTION
Differential Element:The mass of the disk element shown shaded in Fig. ais
Mass: The mass of the solid can be determined by integrating dm.Thus,
Mass Moment of Inertia: Integrating ,
dIy
Determ
i
ne t
h
e mass moment of
i
nert
i
a of t
h
e so
lid
formed by revolving the shaded area around the axis.The
total mass of the solid is .1500 kg
y
Iy
y
x
z
4m
2m
z
2
y
3
1
––
16
O
1108
10–95.
The slender rods have a mass of 4 kg
>
m. Determine the
moment of inertia of the assembly about an axis
perpendicular to the page and passing through point A.
SOLUTION
Mass Moment of Inertia About An Axis Through A. The mass of each segment
A
100 mm 100 mm
200 mm
*10–96.
The pendulum consists of a 8-kg circular disk A, a 2-kg
circular disk B, and a 4-kg slender rod. Determine the radius
of gyration of the pendulum about an axis perpendicular to
the page and passing through point O.
SOLUTION
The total mass is
O
0.5 m
1 m
0.4 m 0.2 m
A
B
Ans:
1110
10–97.
Determine the moment of inertia of the frustum of the
cone which has a conical depression. The material has a
density of 200 kg>m3.
I
z
SOLUTION
z
0.8 m
0.6 m
0.2 m
Ans:
1111
10–98.
SOLUTION
The pendulum consists of the 3-kg slender rod and the 5-kg
thin plate.Determine the location of the center of mass G
of the pendulum; then find the mass moment of inertia of
the pendulum about an axis perpendicular to the page and
passing through G.
y
G
2m
y
O
Ans:
10–99.
Determine the mass moment of inertia of the thin plate
about an axis perpendicular to the page and passing
through point O.The material has a mass per unit area of
.20 kg>m2
SOLUTION
Composite Parts: The plate can be subdivided into the segments shown in Fig. a.
Mass Moment of Inertia: The mass of segments (1) and (2) are
The mass moment of inertia of the wheel about an axis perpendicular to the
m1=
400 mm
150 mm
400 mm
O
50 mm
50 mm
150 mm
Ans:
1113
*10–100.
SOLUTION
T
he pendulum consists of a plate having a weight of 12 lb
a
nd a slender rod having a weight of 4 lb.Determine the
r
adius of gyration of the pendulum about an axis
p
erpendicular to the page and passing through point O.
O
2ft
3ft
1ft
1ft
1114
10–101.
SOLUTION
Composite Parts:The wheel can be subdivided into the segments shown in Fig. a.
Mass Moment of Inertia: First, we will compute the mass moment of inertia of the
If the large ring,small ring and each of the spokes weigh
100 lb,15 lb,and 20 lb,respectively,determine the mass
moment of inertia of the wheel about an axis perpendicular
to the page and passing through point A.
A
O
1ft
4ft
Ans:
1115
10–102.
Determine the mass moment of inertia of the assembly
about the zaxis.The density of the material is 7.85 Mg m3.
SOLUTION
Composite Parts: The assembly can be subdivided into two circular cone segments (1)
Mass: The mass of each segment is calculated as
Mass Moment of Inertia: Since the zaxis is parallel to the axis of the cone and the
>z
100 mm
1116
10–103.
SOLUTION
Each of the three slender rods has a mass m. Determine the
moment of inertia of the assembly about an axis that is
perpendicular to the page and passes through the center
point O.
O
a
a
Ans:
*10–104.
SOLUTION
Composite Parts:The thin plate can be subdivided into segments as shown in Fig. a.
The thin plate has a mass per unit area of .
Determine its mass moment of inertia about the yaxis.
10 kg
>
m
2
200 mm
200 mm
200 mm
200 mm
200 mm
z
x
100 mm
100 mm
Ans:
1118
10–105.
The thin plate has a mass per unit area of .
Determine its mass moment of inertia about the zaxis.
10 kg>m
2
SOLUTION
200 mm
200 mm
200 mm
200 mm
z
100 mm
100 mm
10–106.
SOLUTION
Determine the moment of inertia of the assembly about an
axis
that is perpendicular to the page and passes through
the
center of mass G.The material has a specific weight of
.
g
=90 lb>ft3
O
1ft
2ft
0.5 ft
G
0.25 ft
10–107.
Determine the moment of inertia of the assembly about an
axis that is perpendicular to the page and passes through
point O.The material has a specific weight of .g=90 lb>ft3
SOLUTION
O
1ft
2ft
G
0.25 ft
1121
*10–108.
SOLUTION
T
h
e pen
d
u
l
um cons
i
sts of two s
l
en
d
er ro
d
s AB an
d
OC
which have a mass of The thin plate has a mass of
Determine the location of the center of mass G
of the pendulum, then calculate the moment of inertia of
the pendulum about an axis perpendicular to the page and
passing through G.
y
12 kg>m2.
3kg>m.
AB
G
O
1.5
m
0.4 m 0.4 m
_
y
1122
10–109.
Determine the moment of inertia of the frustrum of the
cone which has a conical depression. The material has a
density of 200 kg>m3.
I
z
SOLUTION
Mass Moment of Inertia About z Axis:From similar triangles,
z
0.2 =z+1
0.8 ,
z
200 mm
800 mm
600 mm
400 mm