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King James (Cubs Suk, Go Cards)
King James (Cubs Suk, Go Cards) asked in Science & MathematicsPhysics · 6 years ago

Physics Question. Meter Stick and rotational motion.?

Update:

A meter stick is held to a wall by a nail passing through the 60-cm mark. The meter stick is free to swing about this nail, without friction. If the meter stick is released from an initial horizontal position, what angular velocity will it attain when it swings through the vertical position?

1 Answer

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  • NCS
    Lv 7
    6 years ago

    Easiest as an energy problem.

    Relative to the vertical position, the initial potential energy is

    PE = mgh = M * 9.8m/s² * 0.10m = M * 0.98m²/s²

    This gets converted into KE:

    KE = M * 0.98m²/s² = ½Iω²

    By the parallel axis theorem,

    I = ML²/12 + Md² = M((1m)²/12 + (0.10m)²) = M * 0.093m², so

    M * 0.98m²/s² = ½ * M * 0.093m² * ω² → M cancels

    ω² = 21 /s²

    ω = 4.6 rad/s

    Hope this helps!

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