# dynamics

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** ∝ *m***a**, 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** = *m***a**. (See also momentum.)

Newton suggested that gravitational attraction existed between all bodies,
and proposed a law to describe this: if two bodies, masses *m*_{1} and *m*_{2}, are separated by a distance *d*, the
force of attraction, **F**, between them is given by **F** = G(*m*_{1}*m*_{2})/*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** = *m***g**, where **g** is another constant,
the acceleration due to gravity (usually
denoted *g* although it is a vector).