Newtonian Mechanics

The position of a body is a function of the time. It can be expressed in terms of three coordinates, for example, how far East, North, and Up it is from an arbitrarily chosen origin. (A distance South is just a negative distance North.)

The rate of change of the position is called the velocity. It includes both magnitude (aka speed) and direction.

The rate of change of the velocity is called the acceleration. It also includes both magnitude and direction.

If you know where a body is at some instant and you also know its velocity, you can calculate where it will be a very short time later.

If you know the velocity of a body at some instant and you also know its acceleration, you can calculate its velocity a very short time later.

According to Newton, the acceleration of a body is simply the net force acting on it divided by its mass.

The net force acting on a body is the vector sum of all of the forces acting on the body. For two forces it is the diagonal of the parallelogram formed by representing them as arrows.

Newton was able to explain all motions in the sky using just the above and a universal force, called gravitation, which acts between any two bodies. This force is proportional to the mass of each and inversely proportional to the square of the distance between them.

The same set of laws apply to motions on earth. All that is needed is to include some other forces, such as friction, in addition to the gravitational force.

Please send comments, additions, corrections, and questions to
joe.tenn@sonoma.edu

JST

2002-09-19