Moment of inertia

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Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion.





Moment of inertia is defined with respect to a specific rotation axis. The moment of inertia of a point mass with respect to an axis is defined as the product of the mass times the distance from the axis squared. The moment of inertia of any extended object is built up from that basic definition. The general form of the moment of inertia involves an integral.





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However, in the study of Newtonian Mechanics, Newtons law of motion applies not only to translational linear motion but also to rotational motion of a rigid body. The interpretation of the rotational form of Newtons law for a rigid body about an axis is in the form


= I


Net external torque = moment of inertia x angular acceleration


where is the torque, is the angular acceleration, and I is the mass moment of inertia about a reference axis.


The relationship between the net external torque and the angular acceleration is of the same form as Newtons second law and is sometimes called Newtons second law for rotation. It is not as general a relationship as the linear one because the moment of inertia is not strictly a scalar quantity. The rotational equation is limited to rotation about a single principal axis, which in simple cases is an axis of symmetry.


Just as mass is a measure of inherent property of resistance to translation, moment of imertia is a measure of inherent tendency to resist rotational motion. Otherwise known as the second moment of mass, moment of inertia serves as a resistance towards rotational motions of rigid bodies. However, it is more difficult to appreciate the physical significance of the second moment of mass than the first moment of mass. From this experiment, the effect and determination of moment of inertia in rigid body motion will be demonstrated and investigated.





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