Page 301 - Dynamics of Mechanical Systems

0593_C09_fm Page 282 Monday, May 6, 2002 2:50 PM

282 Dynamics of Mechanical Systems

where the final expression is obtained by recognizing M as the total mass of the particles
of B and by recalling that G is the mass center of B so that:

N
∑ m r = 0 (9.3.6)
ii
i=1
(See Section 6.8.)
Equation (9.3.5) shows that for a rigid body the computation of the linear momentum
is in essence as simple as the computation of linear momentum for a single particle as in
Eq. (9.3.1).

9.4 Angular Momentum
Consider again a particle P having mass m and velocity v in a reference frame R as in
Figure 9.4.1. Let Q be an arbitrary reference point. Then, the angular momentum A of P
Q
about Q in R is defined as:
D
×
A = p m v (9.4.1)
Q
where p locates P relative to Q. Observe that A has the units mass–length–velocity, or
Q
mass–(length) per unit time.
2
Angular momentum is sometimes called moment of momentum. Indeed, if we recognize
mv as the linear momentum L of P, we can write Eq. (9.4.1) in the form:
×
A = p L (9.4.2)
Q
Consider next a set S of N particles P (i = 1,…, N) having masses m and velocities v P i in
i i
R as in Figure 9.4.2. Again, let Q be an arbitrary reference point. Then, the angular
momentum of S about Q in R is defined as:

N
SQ ∑ P i
A = p × m i v (9.4.3)
i
i=1
where p locates P relative to Q.
i i
Finally, consider a rigid body B with mass m and mass center G moving in a reference
frame R as in Figure 9.4.3. Consider B to be composed of N particles P with masses m
i i

FIGURE 9.4.1
A particle P with mass m, velocity v, and
reference point Q.