## SF1 22 2mi ai33

In this equation, SF1 denotes the sum of external forces acting on B (external contact forces plus the gravitational body force). The term 22fij is

mk g

Figure 3.1. A system of particles (B) moving with respect to reference frame E. Particles in B were marked with rectangles and particles outside of B with filled circles. The position vectors r!/o, r!/c, and rc/o connect, respectively, the point O to particle i, the center of mass C to point i, and point O to the center of mass C. Also shown in the figure are internal forces fj and 1 fji and external forces Fj and mk g.

the sum of all internal forces acting on particles in B. Newton's third law requires that this latter sum be equal to zero. Thus, internal forces do not contribute to the acceleration of the system at all and hence Eqn. 3.3 assumes the following form:

Linear momentum L of a system of particles B is defined as

where v1 denotes the velocity of particle i. Combining Eqns. 3.4 and 3.5, we obtain

This equation is called the conservation of linear momentum. According to this equation, the time rate of change of linear momentum of a system of particles is equal to the resultant external force acting on the system. When a body is at rest or moving with constant speed, its linear momentum remains constant and hence the sum of all forces acting on the body must vanish. The branch of mechanics that considers bodies in equilibrium is called statics. Later in the text, in Chapters 5 and 6, we discuss statics as it relates to human movement.

## Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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