The following concept map for Newton's second law of motions illustrates the power of cognitive condensation.

This map clearly shows that one can learn a tremendous amount of science, mathematics, and technology by judiciously organizing knowledge using causal, logical, and functional relationships and by making only statements that are correct in their generalities or contain specifications of the limits of their applicability.

Please see how Newton's second law, correctly stated in terms of the linear momentum, directly leads to the law of conservation of the linear momentum (for a single particle of the total linear momentum for a system of particles)

Once this is understood, the treatment of collisions becomes a trivial matter provided that the key characteristic property of collisions is known: for all collisions (from K to the Ph.D.) we assume the sum of the external forces to be zero!

Please note that the correct statement of Newton's second law directly leads to the popular A correctly stated Newton's second law also leads to the understanding of impulse

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