Dynamics is the branch of mechanics that deals with the behavior of bodies under the action of forces that produce changes of motion in them. Dynamics is based on Newton's three laws of motion: that a body continues in its state of motion unless compelled by a force to act otherwise; that the rate of change of motion (acceleration) is proportional to the applied force and occurs in the direction of the force; and that every action is opposed by an equal and opposite reaction. The first gives an idea of inertia, which is proportional to the mass and opposes the change of motion: combining the first with the second, we find that F ∝ ma, where F is the force, m the mass of the body, and a the acceleration produced by the force. In practice, units are chosen such that F = ma. (See also momentum.
Newton suggested that gravitational attraction existed between all bodies, and proposed a law to describe this: if two bodies, masses m1 and m2, are separated by a distance d, the force of attraction, F, between them is given by F = G(m1m2)/d 2, where G is the universal gravitational constant (see gravity). Near the surface of the Earth we fond for a body of mass m that F ∝ m (G and the mass of the Earth are constant and the distance from the surface to the center is approximately so.) We usually set F = mg, where g is another constant, the acceleration due to gravity (usually denoted g although it is a vector).