The basic notions of classical physics concern particles moving in straight lines, or linear motion. The concepts of linear motion are usually grouped into two categories, kinematics and dynamics. Kinematics deals with predicting the position of a particle if its position, velocity, and acceleration at some reference time (usually set to be t =0) is known. Velocity is the rate of change of position with respect to time, and acceleration is the rate of change of velocity with respect to time. The two kinematical equations are, for constant acceleration: v(t) = v + at, and x(t) = x + vt + 1/2 at2 , where x is the position, v is the velocity (the subscripted v indicates the velocity at the start or origin), a is the acceleration, and t is understood as the change in time.
Dynamics deals with how kinematical quantities such as velocity and acceleration react to forces. The basic dynamic rule is Newton's second law, which says that the acceleration of a particle is equal to the sum of all external forces on the particle, divided by the mass of the particle: a = F/m. Equally important rules are the conservation of energy, and linear momentum. Conservation of energy states that as long no external forces are acting, the energy of a system of particles is constant, although it may change forms. Conservation of linear momentum states that if the momenta of all particles in a system is added, it is a constant, although the momentum may become differently distributed among the particles. Again, this principle works only if there are no external forces acting on the system. These rules allow us to analyze particles under the influence of external forces and particles colliding into each other.
Often particles are not moving in straight lines. In this case, the particle's motion can be separated into two components, which are straight lines. These components can be analyzed individually. For example, when a cannon is shot into the air at an angle, it has motion parallel to the ground and also motion perpendicular to the ground. The projectile motion of the cannonball can thus be analyzed in terms of these two sets of variables, both of which exhibit linear motion.
Because linear motion is well understood, other sorts of motion often treated by approximating the motion as linear for a short time. An example is rotational motion, where particles travel in circles around a central point. The kinematical and dynamic equations for rotational motion are translated and transformed from the linear systematics.
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