|Asia-Pacific Forum on Science
Learning and Teaching, Volume 4, Issue 2, Article 8 (Dec., 2003)
On using Geometer's Sketchpad to teach relative velocity
Example 3: Concept of the actual system and relative system
The method of teaching Relative Velocity is usually the "Reduction to Rest" method, see National Institute of Education 2003, Pp 186-189. In a system when two particles A and B are moving with constant velocity, it is equivalent to another system where one of the particle (say B) is resting while A is traveling with the relative velocity of A with respect to B. The former system is called the "Actual System" while the latter system the "Relative System with respect to B".
The question which naturally arises is: why are these two systems equivalent? From the geometry point of view, it is just a translation of the origin to the point A, which is supposed to be reduced to rest. However, this is abstract for most students as it implicitly involves translation of the system. With the use of animation, the concept of equivalence can be easily brought out.
Figure 6 shows the case when both the Actual System and the Relative System (B reduced to rest) are shown in parallel. As the animation button is clicked, both systems will start to move (as in Figure 7). In the Actual system, both particles A and B move whereas in the Relative Velocity, only particle A moves while B is at rest.
Students will observe that at any point in time, the vector AB, the relative displacement of A from B, in either the Actual System and the Relative System are equal.
Students can change the initial points of A and B by dragging them to different positions, but the vectors AB in both the Actual System and Relative System will always be equal, regardless of whether A and B are in motion or stationary. The physical meaning of the Relative System is clearly brought out. This is an alternative approach to mechanically "converting" the Actual System into the Relative System by reducing B to rest.
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