Page 467 - Introduction to Continuum Mechanics

Principle of Moment of Momentum 451

i.e.,

This equation can be written

If at t = 0, x = 0, then

7.9 Principle of Moment of Momentum
The global principle of moment of momentum states that the total moment about a fixed
point, of surface and body forces on a fixed part of material is equal to the time rate of change
of total moment of momentum of the part about the same point. That is,

where x is the position vector for a particle.

Using the Reynold's transport theorem, Eq. (7.4.2), the left side of Eq. (7.9.1) becomes

Since

therefore the integrand in Eq. (i) becomes

Thus

Also, from Example 7.2.2 of this chapter, we have