978-0077687342 Appendix B Part 1

subject Type Homework Help
subject Pages 14
subject Words 1352
subject Authors Brian Self, E. Johnston, Ferdinand Beer, Phillip Cornwell

Unlock document.

This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
page-pf1
APPENDIX B
page-pf2
PROBLEM B.1
A thin plate of mass m is cut in the shape of an equilateral triangle of side a.
Determine the mass moment of inertia of the plate with respect to (a) the
centroidal axes AA and BB, (b) the centroidal axis CC that is perpendicular
to the plate.
SOLUTION
13 3


12
page-pf3
PROBLEM B.2
A ring with a mass m is cut from a thin uniform plate. Determine the
mass moment of inertia of the ring with respect to (a) the axis AA, (b) the
centroidal axis CC that is perpendicular to the plane of the ring.
CC AA BB AA
12
2
CC
page-pf4
PROBLEM B.3
A thin, semielliptical plate has a mass m. Determine the mass moment of
inertia of the plate with respect to (a) the centroidal axis BB, (b) the
centroidal axis CC that is perpendicular to the plate.
4
page-pf5
PROBLEM B.4
The parabolic spandrel shown was cut from a thin, uniform plate.
Denoting the mass of the spandrel by m, determine its mass
moment of inertia with respect to (a) the axis BB, (b) the axis
DD that is perpendicular to the spandrel. (Hint: See Sample
Problem 9.3.)
,area 11 ,area
4
AA


page-pf6
PROBLEM B.4 (Continued)
2
1

710
70
page-pf7
PROBLEM B.5
A piece of thin, uniform sheet metal is cut to form the machine
component shown. Denoting the mass of the component by m,
determine its mass moment of inertia with respect to (a) the x axis,
(b) the y axis.
,mass 2
2
48
3
31
72
z
a
ma
page-pf8
PROBLEM B.5 (Continued)
Finally, ,mass ,mass ,mass
yxz
III

y
page-pf9
PROBLEM B.6
A piece of thin, uniform sheet metal is cut to form the machine
component shown. Denoting the mass of the component by m,
determine its mass moment of inertia with respect to (a) the axis
AA, (b) the axis BB, where the AA and BB axes are parallel to the
x axis and lie in a plane parallel to and at a distance a above the xz
plane.
SOLUTION
page-pfa
PROBLEM B.7
A thin plate of mass m has the trapezoidal shape shown. Determine
the mass moment of inertia of the plate with respect to (a) the x
axis, (b) the y axis.
SOLUTION
18 ma
,mass
y
page-pfb
PROBLEM B.8
A thin plate of mass m has the trapezoidal shape shown. Determine
the mass moment of inertia of the plate with respect to (a) the
centroidal axis CC that is perpendicular to the plate, (b) the axis
AA that is parallel to the x axis and is located at a distance 1.5a
from the plate.
page-pfc
PROBLEM B.8 (Continued)
From the solution to Problem 9.193:
2
5
,mass
18 9
AA




or
2.33
AA
Ima
page-pfd
PROBLEM B.9
Determine by direct integration the mass moment of inertia
with respect to the z axis of the right circular cylinder shown,
assuming that it has a uniform density and a mass m.
12
z
page-pfe
PROBLEM B.10
The area shown is revolved about the x axis to form a
homogeneous solid of revolution of mass m. Using direct
integration, express the mass moment of inertia of the solid
with respect to the x axis in terms of m and h.
SOLUTION
2
hh
10 7 70
x


or
1.329
x
Imh
page-pff
PROBLEM B.11
The area shown is revolved about the x axis to form a
homogeneous solid of revolution of mass m. Determine by
direct integration the mass moment of inertia of the solid with
respect to (a) the x axis, (b) the y axis. Express your answers in
terms of m and the dimensions of the solid.
3
33
44 4
22 2
223
111126
63 627
1 2 13 13
63 9 54
xx
aa
xx
ah ah
aa
ah h mh
 

 
  


  





  

or
0.241
x
Imh
page-pf10
PROBLEM B.11 (Continued)
y
page-pf11
PROBLEM B.12
Determine by direct integration the mass moment of inertia with
respect to the x axis of the tetrahedron shown, assuming that it has
a uniform density and a mass m.
SOLUTION

ay
page-pf12
PROBLEM B.12 (Continued)
10
x
page-pf13
PROBLEM B.13
Determine by direct integration the mass moment of inertia with
respect to the y axis of the tetrahedron shown, assuming that it has
a uniform density and a mass m.
SOLUTION

ay
,mass ,mass
12 12
BB DD
 
 
page-pf14
PROBLEM B.13 (Continued)
10
y

Trusted by Thousands of
Students

Here are what students say about us.

Copyright ©2022 All rights reserved. | CoursePaper is not sponsored or endorsed by any college or university.