4 NEWTON’S LAWS OF MOTION 4.9 Frames of referencef m^
mg sinmg cos
mg
mg cos (^)
Figure 33: Block sliding down a rough slope
reaction at the surface. Once the object has been set in motion, the frictional force
acting to impede this motion falls somewhat to μk times the normal reaction.
4.9 Frames of reference
As discussed in Sect. 1 , the laws of physics are assumed to possess objective real-
ity. In other words, it is assumed that two independent observers, studying the
same physical phenomenon, would eventually formulate identical laws of physics
in order to account for their observations. Now, two completely independent
observers are likely to choose different systems of units with which to quantify
physical measurements. However, as we have seen in Sect. 1 , the dimensional
consistency of valid laws of physics renders them invariant under transformation
from one system of units to another. Independent observers are also likely to
choose different coordinate systems. For instance, the origins of their separate
coordinate systems might differ, as well as the orientation of the various coordi-
nate axes. Are the laws of physics also invariant under transformation between
coordinate systems possessing different origins, or a different orientation of the
various coordinate axes?
Consider the vector equation
r = r 1 + r 2 , (4.26)
which is represented diagrammatically in Fig. 12. Suppose that we shift the origin