FirstPrinciplesa Physoly project
EN-03energytrap · Vector / scalar confusion

Kinetic energy is a scalar — it has no direction

  1. 01

    The tempting model

    Assigning a direction to KE or adding energies as vectors.

  2. 02

    Why it feels right

    Motion has a direction, so its energy seems to as well.

  3. 03

    Where it breaks · how to catch it

    You wrote a negative KE or split energy into components.

  4. 04

    The correct model

    KE = ½mv² depends on speed squared — always ≥ 0 and directionless. Momentum, not energy, carries direction.

  5. 05

    Repair · see it, then test it

    worked example Two balls, equal speed, opposite directions. Total kinetic energy?

    Tempting move

    Zero — they cancel.

    Correct move

    2 × ½mv²; energies add as positive scalars.

    Test the repair EN-03 · transfer
    A 1 kg puck moves east at 2 m/s and another 1 kg puck moves west at 3 m/s. Their total kinetic energy is:

    Make a fresh prediction before referring to the worked example.