Conservation of mechanical energy is assumed if kinetic energy
(T) and potential energy (V) change back and forth in a conservative
system (the dissipation of energy is considered negligible). Equation
1.3.22 formalizes such a situation, where position 1 is the initial state
and position 2 is the ?nal state. The reference (datum) should be chosen to
reduce the number of terms in the equation.

T₁ + V₁ = T₂ + V₂

Linear and Angular Momentum Methods

The concept of linear momentum is useful in engineering when the
accelerations of particles are not known but the velocities are.
The linear momentum is derived from Newtons second law,

G  = mv

The time rate of change of linear momentum is equal to force.
When mv is constant, the conservation of momentum equation results,

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The work and energy equation for a system of particles is similar to the
equation stated for a single particle.

Momentum Methods for a System of Particles

Moments of Forces on a System of Particles. The moments of
external forces on a system of particles about a point O are given by

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General plane motion of a rigid body is de?ned by simultaneous
translation and rotation in a plane. Figure 1.3.11 illustrates how the velocity
of a point A can be determined using Equation 1.3.46, which is based on
relative motion of particles.

FIGURE 1.3.11 Analysis of velocities in general plane motion.
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