Page 250 - Dynamics of Mechanical Systems

0593_C07_fm Page 231 Monday, May 6, 2002 2:42 PM

Inertia, Second Moment Vectors, Moments and Products of Inertia, Inertia Dyadics 231

P7.2.2: See Problem P7.2.1. Let point Q have coordinates (–1, 2, 4). Repeat Problem P7.2.1
with Q, instead of O, being the reference point. That is, find I PQ I , PQ I , PQ I , PQ , and I PQ .
x y z a b
P7.2.3: Consider the system S of two particles P and P located on the X-axis of a Cartesian
2
1
coordinate system as in Figure P7.2.3. Let the masses of P and P be m and m , and let
2
1
2
1
the distances of P and P from the origin O be x and x . Find the second moment of P
1
2
1
2
relative to O for the direction of n . (Observe that I S O is parallel to n .)
y
y
y
Y
n y
P (m ) P (m )
2 2 x 2 x 1 1 1
FIGURE P7.2.3 O X
Particles P 1 and P 2 on the X-axis of a
Cartesian reference frame. n x
P7.2.4: See Problems P7.2.1 and P7.2.3. Find a unit vector n such that I PO is parallel to n.
n
P7.2.5: Let a set S of three particles P , P , and P be located at the vertices of a triangle as
1 2 3
shown in Figure P7.2.5. Let the particles have masses 2, 3, and 4 kg, respectively. Find
I SO I , SO , and I SO where as before O is the origin of the x, y, z coordinate system of Figure
x x z
P7.2.5, and n , n , and n are the unit vectors shown.
x y z
Z
P (2,2,4)
n z 2

P (0,5,2)
3
O P (1,1,1) Y
1
n y

FIGURE P7.2.5
Particles at the vertices of a triangle. X n x

P7.2.6: See Problem P7.2.5. Let n and n be unit vectors with coordinates relative to n ,
a
b
x
n , and n as:
z
y
.
.
n = 0 75 n − 0 5 n + 0 433 n
.
a x y z
and
n = 0 655 n + 0 756 n
.
.
b y z
Determine I SO and I SO .
a b
P7.2.7: See Problems P7.2.5 and P7.2.6. Show that:
I SO = 0 75 I SO − 0 50 I SO + 0 433 I SO
.
.
.
a x y z