Moment of inertia (I) in rotatory motion is similar to effect mass of the body in transitory motion.This physical quantity opposes the rotatory motion of the body and to overcome this we need to apply torque.
I is independent of the magnitude of the angular velocity. It is a characteristic of the rigid body and the axis about which it rotates. In rotation (about a fixed axis), the moment of inertia plays a similar role as mass does in linear motion.
As the mass of a body resists a change in its state of linear motion, it is a measure of its inertia in linear motion. Similarly, as the moment of inertia about a given axis of rotation resists a change in its rotational motion, it can be regarded as a measure of rotational inertia of the body; it is a measure of the way in which different parts of the body are distributed at different distances from the axis.
Unlike the mass of a body, the moment of inertia is not a fixed quantity but depends on the orientation and position of the axis of rotation with respect to the body as a whole. As a measure of the way in which the mass of a rotating rigid body is distributed with respect to the axis of rotation.
The radius of gyration of a body about an axis may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis.
Thus, the moment of inertia of a rigid body depends on the mass of the body, its shape and size; distribution of mass about the axis of rotation, and the position and orientation of the axis of rotation.(24)
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I is independent of the magnitude of the angular velocity. It is a characteristic of the rigid body and the axis about which it rotates. In rotation (about a fixed axis), the moment of inertia plays a similar role as mass does in linear motion.
As the mass of a body resists a change in its state of linear motion, it is a measure of its inertia in linear motion. Similarly, as the moment of inertia about a given axis of rotation resists a change in its rotational motion, it can be regarded as a measure of rotational inertia of the body; it is a measure of the way in which different parts of the body are distributed at different distances from the axis.
Unlike the mass of a body, the moment of inertia is not a fixed quantity but depends on the orientation and position of the axis of rotation with respect to the body as a whole. As a measure of the way in which the mass of a rotating rigid body is distributed with respect to the axis of rotation.
The radius of gyration of a body about an axis may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis.
Thus, the moment of inertia of a rigid body depends on the mass of the body, its shape and size; distribution of mass about the axis of rotation, and the position and orientation of the axis of rotation.(24)
Related posts :
Friction introduction Rolling Friction Newton's First law of motion Newton's second law of motion Newton's third law of motion Common Forces in mechanics Free body diagram Circular motion part one and two
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