FirstPrinciplesa Physoly project
MOM-07momentumtrap · Vector / scalar confusion

Momentum components conserve separately

  1. 01

    The tempting model

    Conserving the speed-like magnitude of momentum instead of x and y components.

  2. 02

    Why it feels right

    Momentum is introduced as p = mv, so it can look like one scalar amount.

  3. 03

    Where it breaks · how to catch it

    A two-dimensional collision is solved with one momentum equation using magnitudes.

  4. 04

    The correct model

    Momentum is a vector. If external impulse is negligible, conserve p_x and p_y independently.

  5. 05

    Repair · see it, then test it

    worked example A puck moving east breaks into two pieces, one moving north. What must the other piece do?

    Tempting move

    Move south with the same speed.

    Correct move

    Its momentum must supply both the original east component and a south component to cancel the north piece.

    Test the repair MOM-07 · transfer
    A system starts with momentum (8, 0) kg·m/s. After an internal separation, one piece has (3, 4) kg·m/s. The other piece has:

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R22Two-dimensional momentumadds: Momentum conserves by component.