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0593_C09_fm Page 313 Monday, May 6, 2002 2:50 PM

Principles of Impulse and Momentum 313

TABLE P9.4.4

Kinematic and Inertial Properties of Particles P i
i m i x i y i z i v ix v iy v iz
1 2 1 –2 4 6 –2 3
2 1 8 3 –2 –3 5 2
3 3 –9 4 5 6 –4 8
4 4 –4 –7 6 –5 1 4
5 6 5 6 –4 3 6 –1

P9.4.6: See Problem P9.4.4. Show that the particles P of S, with velocity components as
i
listed in Table P9.4.4, are not fixed on a rigid body B. (Hint: Select any two particles, say
1 /
P and P , and show that V PP 2 ⋅ P P ≠ 0. )
1
2
12
P9.4.7: See Problems P9.4.4 to P9.4.6. Suppose the particles of Problem P9.4.4 are fixed
relative to one another so that they form a rigid body B. Then, in view of Problem P9.4.6,
the velocity components listed in Table P9.4.4 are no longer valid but instead are unknown,
as represented in Table P9.4.7. Let G be the mass center of S (see Problem P9.4.5) and let
G
G have velocity V given by:
G
V = 5 n − 3 n + 7 n m s
x y z
Let B have angular velocity ω given by:

ωω= 3n − 2n + 4n rad sec
x y z

Find (a) the velocities of P (i = 1,…,5) relative to G, and (b) the velocities of P relative to O.
i
i
TABLE P9.4.7
Position and Inertial Properties of Particles P i
i m i x i y i z i v ix v iy v iz
1 2 1 –2 4 Unknown (to be determined)
2 1 8 3 –2 Unknown (to be determined)
3 3 –9 4 5 Unknown (to be determined)
4 4 –4 7 6 Unknown (to be determined)
5 6 5 6 –4 Unknown (to be determined)

P9.4.8: See Problems P9.4.4 to P9.4.7. Use the conditions and results of Problem P9.4.7 to
find the angular momentum of S relative to O, A S/O ; and the angular momentum of S
relative to G, A .
S/G
P9.4.9: See Problems P9.4.4 to P9.4.8. Let G have a mass of 16 kg. Find the angular
momentum of G relative to O, A G/O .
P9.4.10: See Problems P9.4.8 and P9.4.9. Show that:

A = A + A
SO S G G O

(See Eq. (9.4.14).)