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Dynamics is the branch of mechanics dealing with the motion of bodies (kinematics) and the action of forces in producing or changing their motion. The accelerated motion of bodies is described by the Newton’s three laws of motion.

Newton’s laws of motion

First law (law of inertia)
A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided that the particle is not subjected to an external force.

Second law (motion law)
If a particle of mass m is subjected to a force F, then this particle experiences an acceleration a with the same direction and sense as the force and a magnitude that is proportional to the force: F = ma.

Third law (action-reaction principle)
If a particle is subjected to a force F, this force results from the interaction with a second particle that is subjected to a force -F equal in module and direction and opposite in sense.

Dynamic Equilibrium

If an object is subjected to several forces F_i (i = 1, n) the acceleration of the object is directly proportional to the magnitude of the net force F = Σ F_i, in the same direction as the net force, and inversely proportional to the mass of the object: F = Σ F_i = ma.

In Figure 1 a particle of mass m is subjected to two forces F₁ and F₂. The second law must be interpreted as: F₁ + F₂ = F = ma, where F is the sum of the two forces.

Figure 1: Dynamic equilibrium