8.2 Newton's second law of motion  (Page 4/5)

Actually second law is defined in the context of translational motion, in which a three dimensional real body behaves like a point. We shall subsequently learn that application of a force system (forces) on a body in translation is equivalent to a point, where all mass of the body can be considered to be concentrated. In that case, the acceleration of the body is associated with that point, which is termed as “center of mass (C)”. The Newton's second law is suitably modified as :

where $a_c$ is the acceleration of the center of mass (we shall elaborate about the concept of center of mass in separate module). In general, application of a force system on a real body can involve both translational and rotational motion. In such situation, the concurrency of the system of forces with respect to points of application on the body assumes significance. If the forces are concurrent (meeting at a common point), then the force system can be equivalently represented by a single force, applied at the common point. Further, if the common point coincides with “center of mass (C)”, then body undergoes pure translation. Otherwise, there is a turning effect (angular/rotational effect) also involved.

Concurrent force system

What if the forces are not concurrent? In this case, there are both translational and rotational effects to be considered. The translational motion is measured in terms of center of mass as in pure translation, whereas the turning effect is studied in terms of “moment of force” or “torque”. This is defined as :

Non-concurrent force system

where $r_{\perp }$ is perpendicular distance from the point of rotation.

Most importantly, same force or force system is responsible for both translational effect (force acting as "force" as defined by the second law) and angular/rotational effect (force manifesting as "torque" as defined by the angular form of Newton's second law in the module titled Second law of motion in angular form ). We leave the details of these aspects of application of force as we will study it separately. But the point is made. Linear acceleration is not the only “effect” of the application of force (cause).

Also, force causes “effect” not necessarily as cause of acceleration – but can manifest in many ways : as torque to cause rotation; as pressure to change volume, as stress to deform a body etc. We should, therefore, always keep in mind that the study of translational effect of force is specific and not inclusive of other possible effects of force(s).

In the following listing, we intend to clarify the context of the study of the motional effect of force :

1: The body is negligibly small to approximate a point. We apply Newton’s second law for translation as defined without any consideration of turning effect.

2: The body is a real three dimensional entity. The force system is concurrent at a common point. This common point coincides with the center of mass. We apply Newton’s second law for translation as defined without any consideration of turning effect. Here, we implicitly refer the concurrent point as the center of mass.