PROBLEM 18.7 (Continued)
For each plate parallel to the xy plane: 1
5
mm
2
2
222
111
12 12 12
y
a
Imam mama
Total moments of inertia:
22
22
13 1 7 37
111 3
(37) (36) (37) 0.43216
60 6
G
Hma
2
0.432
G
Hma
(60)(6)
ma ma
0.43216
G
H
Hω 20.2
PROBLEM 18.8
A thin homogeneous disk of mass m and radius r is mounted
on the horizontal axle AB. The plane of the disk forms an
angle
20
with the vertical. Knowing that the axle rotates
with an angular velocity , determine the angle
formed by
the axle and the angular momentum of the disk about G.
PROBLEM 18.9
Determine the angular momentum HD of the disk of Problem
18.4 about Point D.
PROBLEM 18.4 A homogeneous disk of weight 6lbW
rotates at the constant rate 116
rad/s with respect to arm
ABC, which is welded to a shaft DCE rotating at the constant
rate 28 rad/s.
Determine the angular momentum A
H of the
disk about its center A.
PROBLEM 18.10
Determine the angular momentum of the disk of Problem 18.5 about
Point A.
PROBLEM 18.5
A thin disk of mass
4kgm
rotates at the constant
rate
215 rad/s
with respect to arm ABC, which itself rotates at the
constant rate
15rad/s
about the y axis. Determine the angular
momentum of the disk about its center C.
PROBLEM 18.11
Determine the angular momentum O
H of the disk of Sample Problem 18.2
from the expressions obtained for its linear momentum mv and its angular
momentum HG using Eq. (18.11). Verify that the result obtained is the same
as that obtained by direct computation.
PROBLEM 18.2 A homogeneous disk of radius r and mass m is mounted
on an axle OG of length L and negligible mass. The axle is pivoted at the
fixed Point O, and the disk is constrained to roll on a horizontal floor.
Knowing that the disk rotates counterclockwise at the rate
1 about the axle
OG, determine (a) the angular velocity of the disk, (b) its angular
momentum about O, (c) its kinetic energy, (d) the vector and couple at G
equivalent to the momenta of the particles of the disk.
PROBLEM 18.12
The 100-kg projectile shown has a radius of gyration of 100 mm about
its axis of symmetry
Gx
and a radius of gyration of 250 mm about the
transverse axis
.Gy
Its angular velocity
can be resolved into two
components; one component, directed along
,Gx
measures the rate of
spin of the projectile, while the other component, directed along GD,
measures its rate of precession. Knowing that
6
and that the
angular momentum of the projectile about its mass center G is
2
(500 g m /s)
GHi
2
(10 g m /s) ,j
determine (a) the rate of spin,
(b) the rate of precession.
PROBLEM 18.13
Determine the angular momentum HA of the projectile of Problem
18.12 about the center A of its base, knowing that its mass center G has
a velocity v of 750 m/s. Give your answer in terms of components
respectively parallel to the x and y axes shown and to a third axis z
pointing toward you.
PROBLEM 18.12 The 100-kg projectile shown has a radius of
gyration of 100 mm about its axis of symmetry Gx and a radius of
gyration of 250 mm about the transverse axis .Gy Its angular velocity
can be resolved into two components; one component, directed along
,Gx measures the rate of spin of the projectile, while the other
component, directed along GD, measures its rate of precession.
Knowing that 6
and that the angular momentum of the projectile
about its mass center G is 2
(500 g m /s)
GHi
2
(10 g m /s) ,
j
determine (a) the rate of spin, (b) the rate of precession.
PROBLEM 18.14
(a) Show that the angular momentum B
H of a rigid body about Point B can be obtained by adding to the
angular momentum A
Hof that body about Point A the vector product of the vector
/AB
rdrawn from B to A and
the linear momentum mv of the body:
/BAAB
mHHr v
(b) Further show that when a rigid body rotates about a fixed axis, its angular momentum is the same about
any two Points A and B located on the fixed axis ()
AB
HH
if, and only if, the mass center G of the body is
located on the fixed axis.
PROBLEM 18.15
Two L-shaped arms, each of mass 5 kg, are welded at the one-
third points of the 600 mm shaft AB to form the assembly shown.
Knowing that the assembly rotates at the constant rate of
360 rpm, determine (a) the angular momentum
A
H
of the
assembly about point A, (b) the angle formed by
A
H
and AB.
PROBLEM 18.15 (Continued)
2
3
Gx
Hma
2
32.5 0.2 12
2
2
5.6549 kg m /s
2
1
2
2
1.8850 kg m /s
2
10
3
Gz
3
2
12.5664 kg m /s
Velocity of the mass center: 0
v
(b)
, kHkH
AB AB A A A z
H
22 2 2
cos 13.9085
A
H 25.4