The Nature of the Force Vector

We return to our discussion on Newton's Second Law. Newton describes force by preceding his second law with his first law, stating that without force there is only either constant velocity or zero velocity (staying still). This means that he constructs the idea of "constant velocity" as a possible consequence of a system, in which he calls a balanced system, that has no forces.

Velocity, in this sense, only changes if the system is unbalanced. That means that there can only be a change in velocity, or acceleration that we call it, if there is a force; force and acceleration are a jointed pair. Newton subsequently describes force in an observational manner.

F = m*a

The Object

In order to define what a force is, we have to know what it's acting on; this is the mof the equation. Following from observational information, we know that if an object has more mass, then it is heavier to move. This follows from Newton's Second Law: it's not only that if there is a force then there is an acceleration, the quality of that acceleration is determined by the mass of the object.

Looking at the formula, there is a proportionality relationship here. If the net force is doubled, the acceleration also doubles (assuming we're under constant mass). Additionally, if the mass is doubled, the acceleration is halved (assuming that there is a constantant net force is applied). More force equals more acceleration, and more mass equals less acceleration.

a∝F

a∝1/m

Occasionally, when a system contains more than one object, a collection of objects, or a collection of point particles within a body, can occasionally be treated as a single point-particle, using the equation below.

(x_cm)=(∑_^)((m_i)*(x_i))/(∑_^)((m_i))