What Causes an Acceleration?

So far we have studied some things about acceleration but we never considered what causes things to accelerate. The answer is force. The gravitational force causes objects to fall (i.e. accelerate downwards). Friction force causes cars to slow down (decelerate), etc. Fundamental classical physics is all about finding the force. Once you know that you can get acceleration as we shall see. Once you have the acceleration, you can find velocity, displacement and time as we have studied previously.

Newton's First Law

A body remains in a state of rest, or uniform motion in a straight line, unless acted upon by a force.

Newton's Second Law

Newton's second law of motion is not something we can derive from other equations. Rather it is a fundamental postulate of physics. It was introduced by Isaac Newton to describe the cause of acceleration. The law is

Σ represents the sum (Σ) of all forces () acting on a single body of mass m. The body then undergoes an acceleration given by  One of the key activities in classical physics is to find all the forces Σ. Once you have them then you have the acceleration via  and once you have that you can get velocity, displacement and time. Now Newton's second law is a vector equation. Thus its actual meaning is given by 3 equations, namely

Once we have ΣF_x, ΣF_y, ΣF_z we just divide by m to give the accelerations a_x, a_y, a_z. If they are constant, just plug them into the constant acceleration equations and solve for the other quantities you are interested in. One extra point is the units. The units of a are m/sec². The units of m are kg and thus the units of F are kg m/sec². This is given a special name called Newton (N). Thus

In the English system of units a Pound (lb) is a unit of force. The mass unit is called slug. The units of acceleration are foot/sec². thus

Newton's Third Law

Every action has an equal and opposite reaction.