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But the basic question is to know : why should be look for more than one body system in the first place? It is because such considerations will yield different sets of equations involving laws of motion and thus facilitate solution of the problem in hand.
There is no rule in this regard. However, a suitable coordinate system facilitates easier analysis of problem in hand. The guiding principle in this case is to select a coordinate system such that one of the axes aligns itself with the direction of acceleration and other is perpendicular to the direction of acceleration.
Identifying a suitable coordinate system
For the case as shown in the figure, the coordinate system for body 1 has its x-axis aligned with the incline, whereas its y-axis is perpendicular to the incline. In case, bodies are in equilibrium, then we may align axes such that they minimize the requirement of taking components.
It must be realized here that we are free to utilize more than one coordinate system for a single problem. However, we would be required to appropriately choose the signs of vector quantities involved.
Identifying a suitable coordinate system
In the figure above, we have selected two coordinate systems; one for body 1 and other for body 2. Note that y-axis for body 2 is vertical, whereas y – axis of body 1 is perpendicular to incline. Such considerations are all valid so long we maintain the sign requirements of the individual coordinate systems. In general, we combine "scalar" results from two different coordinate systems. For example, the analysis of force on body 2 yields the magnitude of tension in the string. This value can then be used for analysis of force on body 1, provided string is mass-less and tension in it transmits undiminished.
A free body diagram is a symbolic diagram that represents the body system with a “point” and shows the external forces in both magnitude and direction. This is the basic free-body diagram, which can be supplemented with an appropriate coordinate system and some symbolic representation of acceleration. The free body diagram of body 1 is shown in the upper left corner of the figure :
Constructing a free-body diagram
We may have as many free body diagrams as required for each of the body systems. If the direction of acceleration is known before hand, then we may show its magnitude and direction or we may assign an assumed direction of acceleration. In the later case, the solution finally lets us decide whether the chosen direction was correct or not?
We have discussed in the module titled "Newton's second law of motion" that we implicitly consider force system on a body as concurrent forces. It is so because, Newton's second law of motion connects force (cause) with "linear" acceleration (effect). The words "linear" is implicit as there is no reference to angular quantities in the statement of second law for translation.
We, however, know that such con-currency of forces can only be ensured if we consider point objects. What if we consider real three dimensional bodies? A three dimensional real body involves only translation, if external forces are concurrent (meeting at a common point) and coincides with the "center of mass" of the body. In this situation, the body can be said to be in pure translation. We need only one modification that we assign acceleration of the body to a specific point called "center of mass" (we shall elaborate this aspect in separate module).
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