Force and Newton’s Laws

Isaac Newton’s three laws of motion form the basis of mechanics. These laws explain how forces act and interact. A force is simply defined as “that which causes acceleration”. We measure force in N, or newtons, where .

Forces are vectors, so when added together they can cancel each other out. For example, as I write this I am sitting on a chair. The earth exerts a gravitational force on me (letting the upward direction be positive). However, I am not accelerating (other than my fingers) because the chair gives me a support force, the normal force equal to . Since these forces are in opposite directions but have the same magnitude, they cancel leaving a net force on me . When the net force on something (or someone) is zero, that thing or person is said to be in equilibrium.

Forces are of two types. Forces that act through physical contact, such as the force you exert on a ball when kicking it or on a rocket when launching it, are called contact forces. Forces that act without contact are known as field forces. There are four known field forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. We will study the first two in Physics C, but we first must concern ourselves with contact forces.

Newton’s first law states that if the net force on a particle is zero, the particle has constant velocity. It is more frequently stated as “an object at rest tends to stay at rest, and an object in motion tends to stay in motion in a straight line at constant speed” — an equivalent definition save for the stipulation that the object must have no net force on it.

Newton’s second law is well-known as , but Newton never stated this. Instead, he stated that , where represents momentum. We will discuss momentum in greater detail several lessons from now, but for now it will suffice to know that . The product rule gives and in most cases we will deal with, (i.e., the mass is constant), so that reduces to , the form with which we are all familiar. It is important to remember the original definition, however, when dealing with objects of changing mass such as rockets burning fuel.

Newton’s third law states that whenever an object exerts a force on another, the second object exerts a force equal in magnitude and opposite in direction on the first. This is popularly known as “for every action there is a reaction”.

A common question following from the third law takes the form “If the earth exerts a gravitational force on me that pulls me toward it, why doesn’t my reaction force make the earth gravitate towards me?” Consider, however, that the two forces product a vastly different acceleration. Again, the earth attracts me with a force , and my mass is . If we consider , we have , giving . However, applying the same equation to the earth, which has , we have for . Therefore, while my acceleration towards the earth is perceptible, the earth’s acceleration toward me is far too small to be readily detected.