How to Find the Inertia of an Object

The pendulum can be treated as a solid sphere for calculating inertia.
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Inertia of an object is the resistance offered by the object to change in its motion or position. The inertia is directly proportional to the mass of the object or to the velocity if the object is in motion. According to Newton's first law of motion, an object not subjected to any net external force moves at constant velocity and will continue to do so until some force causes its speed or direction to change. Similarly, an object that is not in motion will remain at rest until some force causes it to move.

    Multiply the mass of the object with the acceleration of the object to get the translational inertia. Translational inertia is a measure of the resistance or opposing force offered by the object in motion when it subjected to a net external force. Simply, it is the resistance that the object will apply to an external opposite force. Translational Inertia = ma, where "m" is the mass, and "a" is the acceleration of the object.

    Calculate the rotational inertia or the moment of inertia by multiplying the mass of the object with square of the distance between the object and the axis, the radius of rotation. Rotational inertia is calculated for objects rotating about an axis. Rotational Inertia = m(r)(r), where "m" is the mass and "r" is the radius or the distance between the object and the axis.

    Calculate the rotational inertia for a solid cylinder or disk of radius "r" and mass "m" by the formula, inertia =1/2(m)(r)(r).

    Calculate the rotational inertia for a thin-shelled hollow sphere of radius "r" and mass "m" by the formula, inertia = 2/3(m)(r)(r).

    Calculate the rotational inertia for a solid sphere of radius "r" and mass "m" by the formula, inertia = 2/5(m)(r)(r).

    Things You'll Need

    • Mass of the object
    • Acceleration of the object
    • Radius of rotational axis

    Tips

    • Use a calculator for complex calculations.

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