Page 251 - Dynamics of Mechanical Systems

0593_C07_fm Page 232 Monday, May 6, 2002 2:42 PM

232 Dynamics of Mechanical Systems

and

.
.
I SO = 0 655 I SO + 0 756 I SO
b y z
P7.2.8: See Problem P7.2.5. Find the x, y, z coordinates of the mass center G of S. Find
SG
I SG , I SG , I SG I , SG , and I .
x y z a b
P7.2.9: See Problem P7.2.8. Let G have an associated mass of 9 kg (equal to the sum of the
masses of P , P , and P ). Find I GO , I GO , I GO I , GO , and I GO .
3
1
2
z
a
y
x
b
P7.2.10: See Problems P7.2.5, P7.2.6, and P7.2.9. Show that:
I SO = I SG + I GO
x x x
I SO = I SG + I GO
y y y
I SO = I SG + I GO
z z z
I SO = I SG + I GO
a a a
and
I SO = I SG + I GO
b b b

P7.2.11: See Problem P7.2.5. Find a unit vector n perpendicular to the plane of P , P , and
1
2
P . Find also I SO . Show that I S O is parallel to n.
3
n
n
Section 7.3 Moments and Products of Inertia
P7.3.1: See Problem P7.2.1. A particle P with mass of 3 slug has coordinates (2, –1, 3),
measured in feet, in a Cartesian coordinate system as represented in Figure P7.3.1. Deter-
mine the following moments and products of inertia: I PO , I PO , I PO I , PO , I PO I , PO I , PO ,
xz
xx
xy
zz
aa
yy
yz
I PO , I PO , and I PO .
bb ab ba

FIGURE P7.3.1
A particle P and a point Q.

P7.3.2: See Problems P7.2.2 and P7.3.1. Let Q have coordinates (–1, 2, 4). Repeat Problem
P7.3.1 with Q, instead of O, being the reference point. That is, determine I PQ , I PQ I , PQ ,
xy
xz
xx
I PQ , I PQ I , PQ I , PQ I , PQ I , PQ , and I PQ .
yy yz zz aa bb ab ba
P7.3.3: See Problem P7.2.5. Let a set S of three particles P , P , and P be located at the
1
3
2
vertices of a triangle as shown in Figure P7.3.3. Let the particles have masses 2, 3, and