Kinetics is that part of dynamics that includes the relationship between forces and any resulting motion.
Newtons second law relates force and acceleration by
F = ma
where the force F and the acceleration a are vectors having the same direction, and the mass m is a scalar.
The acceleration, for example, of a particle of mass m subject to the action of concurrent forces, F1, F2, and F3, can be determined from Eq. (3.24) by resolving each of the forces into three mutually perpendicular directions x, y, and z. The sums of the components in each direction are given by
The magnitude of the resultant of the three concurrent forces is
The acceleration of the particle is related to the force resultant by
The acceleration can then be determined from
In a similar manner, the magnitudes of the components of the acceleration vector a are
provides a condition in dynamics that often can be treated as an instantaneous condition in statics; i.e., if a mass is suddenly accelerated in one direction by a force or a system of forces, an inertia force ma will be developed in the opposite direction so that the mass remains in a condition of dynamic equilibrium. This concept is known as dAlemberts principle.
The principle of motion for a single particle can be extended to any number of particles in a system:
Extension of these relationships permits calculation of the location of the center of mass (centroid for a homogeneous body) of an object:
Concepts of impulse and momentum are useful in solving problems where forces are expressed as a function of time. These problems include both the kinematics and the kinetics parts of dynamics.
By Eqs. (3.29), the equations of motion of a particle with mass m are
Since m for a single particle is constant, these equations also can be written as
The product of mass and linear velocity is called linear momentum. The product of force and time is called linear impulse.
Equations (3.34) are an alternate way of stating Newtons second law. The action of Fx, Fy, and Fz during a finite interval of time t can be found by integrating both sides of Eqs. (3.34):
That is, the sum of the impulses on a body equals its change in momentum.
(J. L. Meriam and L. G. Kraige, Mechanics, Part II: Dynamics, John Wiley & Sons, Inc., New York; F. P. Beer and E. R. Johnston, Vector Mechanics for Engineers Statics and Dynamics, McGraw-Hill, Inc., New York.)