FirstPrinciplesa Physoly project
ROT-03rotationtrap · Rotation / torque-arm error

Moment of inertia depends on the axis

  1. 01

    The tempting model

    Treating I as a fixed property of the object.

  2. 02

    Why it feels right

    Mass is a single number, so rotational inertia seems like one too.

  3. 03

    Where it breaks · how to catch it

    You reused I from a table without matching the axis.

  4. 04

    The correct model

    I depends on how mass is distributed about the chosen axis. Use the parallel-axis theorem I = I_cm + Md² to shift axes.

  5. 05

    Repair · see it, then test it

    worked example A rod spun about its center versus its end — same I?

    Tempting move

    Yes, it's the same rod.

    Correct move

    No: I_end = ML²/3 is four times I_center = ML²/12.

    Test the repair ROT-03 · transfer
    A thin hoop has I = MR² about its central axis. What is I about a parallel tangent axis?

    Make a fresh prediction before referring to the worked example.

    Then practise it on the ladder

    R33Shift the axisadds: Moment of inertia depends on the axis; use parallel-axis theorem.