Force  (Page 4/4)

Contact forces : friction, tension, spring, muscle force etc.

“Action at a distance” forces : gravitational, Electromagnetic

We should understand that “contact” is a relative concept. What appears to be in contact is actually not in contact at atomic or sub-atomic levels. Further, this classification is also in the root of other important classification that divides force types between “fundamental” and “non-fundamental or other force types” :

Fundamental force : gravitational, Electromagnetic, weak force and strong force (nuclear force)

Other force types : friction, tension, spring, muscle force etc.

The important interpretation of this classification is that all other forces are actually macroscopic manifestation of fundamental forces. For example, we push an object with our hand using muscle. This muscle force is a macroscopic outcome of chemical force, which in turn is outcome of electromagnetic force. Also, we should keep in mind that the “effect of force” is same. It either pulls an object or pushes an object. In inertial frame of reference (non-accelerated frame of reference), the effect of force is determined by Newton’s laws of motion.

Newton’s laws of motion and motion types

Newton’s laws of motion form the basic framework in which interaction of force with a particle or a body is studied. As a matter of fact, these are the only laws other than conservation laws which govern whole of kinematics and dynamics i.e. study of motion. Newton’s laws of motion are historically postulated for pure translational motion of a particle and that of a body by extension. We, however, employ a similar set of Newton’s laws for studying rotational motion.

There are three corresponding Newton’s laws of motion for pure rotation. Newton’s first law for rotation, for example, states that a body in rotation remains in rotation unless there is an external torque is applied on it. Similarly, Newton’s second law of motion for rotation relates torque, moment of inertia and angular acceleration as :

$$\mathbf{\tau }=I\mathbf{\alpha }$$

This relation is very much like the famous relation $\mathbf{F}=m\mathbf{a}$ for pure translational motion. Clearly, “force” is replaced by “torque”, “mass” by “moment of inertia” and “linear acceleration” by “angular acceleration”.

Generalization of newton’s laws of motion

We have worked with Newton’s laws with fair degree of accuracy as far as “effect of force” i.e. “change in velocity” i.e. “acceleration" is concerned. It is true when we consider interaction at speeds, which are fraction of the speed of light. At higher speed, it is seen that we need a greater force to accelerate a body than that required to accelerate it by the same degree at a lower speed. The special theory of relativity quantifies (or accounts) this difference. The form of Newton’s law in momentum form remains unaltered even at higher speed and is given by :

$$\begin{array}{l}\mathbf{F}=\frac{đ\mathbf{P}}{đt}\end{array}$$

However, the definition of linear momentum is different at higher speed :

$$\begin{array}{l}\mathbf{P}=\frac{m\mathbf{v}}{\sqrt{(1-\frac{v^2}{c^2}})}\end{array}$$

where “m” is the invariant mass, “v” is velocity and “c” is speed of light. Clearly, the new definition of momentum reduces to classical definition as product of mass and velocity when v<<c. For this reason, we can say that Newton’s laws are subset of more general “special theory of relativity”.

$$\begin{array}{l}\mathbf{P}=m\mathbf{v}\end{array}$$

Unifying theories

The realization that all forces are manifestation of few fundamental forces, gives rise to a temptation to conclude that all fundamental forces may have a unifying origin or model of description. This tempting idea to unify fundamental forces has led many different approaches and models to describe force. The foremost among these has been the successful unification of electrical and magnetic forces via electromagnetic theory. Both these forces are now considered to be manifested due to the presence of charge and its motion. However, no further progress towards unifying other fundamental forces could be made based on this model.

Two promising theories which attempt to unify fundamental forces are “quantum field theory” and “string theory”. The quantum field theory describes force in terms of the exchange of “momentum carrying” particles (photons, bosons etc). According to this theory, the very idea of force is redundant and is replaced by "momentum".