Force  (Page 2/4)

Newton's second law of motion relates force, mass and acceleration. It is important that the measurements of the quantities involved in the relation be same in all inertial frames of reference. Thus, we should be careful while applying Newton’s second law. We must check whether the reference system is inertial or not ? For example, application of Newton’s second law in an accelerated lift will yield unexpected result. Fortunately, this limitation, on the part of reference system, is not insurmountable. We have developed techniques whereupon an accelerated non-inertial reference system can be converted into an equivalent inertial system by applying the concept of pseudo force. Hence, this limitation is not very serious and can be easily overcome.

Generally, we apply laws of motion to the terrestrial objects considering that Earth’s surface is an inertial frame. This assumption, as a matter of fact, is not far from the truth. The Earth rotates about its axis. As such, there is centripetal force working on each objects that we might choose to study. Clearly, the reference system attached to Earth is an accelerated frame - not an inertial frame of reference. But think about the motion of the terrestrial objects. They are confined to relatively smaller dimensions, where centripetal acceleration due to rotation may not cause appreciable or noticeable change in the velocity of the motion being observed. In other words, accounting of centripetal acceleration arising from rotation may not require to be taken care of (using pseudo force).

Force as a vector quantity

Force is a vector quantity. It acts in the direction of application. It is not always possible to identify direction of application in real time situation. As direction of acceleration is same as that of the direction of force, we may identify the direction of force as the direction in which "change of velocity (not velocity alone)" i.e. takes place.

Acceleration or rate of change in velocity takes place considering all forces acting on the body. Force, being vectors, are subject to superposition principle. The superposition principle states that a single vector can represent the effects of all vectors taken together. This single vector is known as net or resultant force.

It is possible that the resultant of the force system working on a body adds up to zero and as such there is no acceleration involved. Two forces may be equal, opposite and collinear and thus canceling each other. Mere existence of forces is not a guarantee of the acceleration od change in velocity. Alternatively, we can also state that absence of acceleration is not a guarantee of absence of force.

The fact, that force is a vector, has yet another important implication. The relation of force (cause) and acceleration (effect) can be studied in three mutually perpendicular directions. This feature of representing vector by components is an experimentally verifiable mathematical construction. In simple words as applied to force vector, acceleration in a given direction can be studied by studying component of force (or forces) in that direction as if other components of force in other mutually perpendicular directions did not exist. This is a great simplification in studying mechanics and must be taken advantage, whenever a situation so presents itself.