Monday, May 30, 2016

Dance of the Changes: ∆p vs. ∆K

Once momentum p and kinetic energy K were derived and the connection between them was established, our task as a class was to find any connections, if any, between ∆p & ∆K. The derivations shown below were conducted in class with the participation of everyone using what I call "Stand/Sit Participation Method". This ensures that every student is active in the derivation process from beginning to end with emphasis on understanding all along.

Students were asked to compare and contrast the two relationships that were derived and only then did the following slide show up.

This, my friends, led to the Free Body Diagrams (FBD) challenges activity that eventually  led to the formulation of Newton's 2nd Law of Motion (N2L.)

A simple harmonic oscillator (SHO) attached to a force probe with a motion detector set below the mass that is attached to the spring provided the conformation of N2L.

The above derivation is aimed at achieving three goals.

1) To help students realize that Physix concepts are not disconnected islands, rather they are individual cells within the organism of Physix knowledge.

2) To establish the emergence of acceleration as a quintessential aspect of any changes in the state of motion of particles.

3) To overemphasize the complementarity between between space and time that relativity asserted and Heisenberg's Uncertainty Principle alluded to in Quantum Mechanics.

Thank you for reading this post and I look forward reading your valuable comments.   

Dedicated to the memory of my beloved father (RA).


  1. What would your students say about why we need two different measures of motion? I ask that question with my students all the time when dealing with momentum and kinetic energy. Mostly they fixate on one being a scalar and one being a vector, but I like to push to point out that just p (and it's magnitude) might be enough. #momentumisking

    1. Indeed, I do get answers from my student that are similar to yours but I did not press any further. Would you, please, share how you take it from that point on? Thank you

    2. I try to push the point that energy is a *very* useful accounting trick for keeping track of momentum swaps. I start with my description of Newton's laws:
      3. momentum is swapped between participants in an interaction
      2. The swap rate is called a force
      1. If you don't swap, it's boring
      Then we talk about where the concept of energy needs to be inserted into that description of the universe. My argument is that maybe it isn't strictly needed. What is needed is an understanding of how the various interactions determine the swap rate (usually based on distance between the participants). Now, of course an energy approach is almost always easiest, but it isn't strictly necessary. I set that table and see what they do with it.