What is moment and product of inertia?
The moment of inertia (I), however, is always specified with respect to that axis and is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis. …
What do the products of inertia mean?
The products of inertia tell us how an object rotates about an axis when a torque is applied about a different axis. In the example above, the product of inertia I x y I_{xy} Ixy tells us how a torque about the x axis affects angular acceleration about the y axis, based on the mass distribution of the object.
What is the use of moment of inertia?
The moment of inertia of an object is a calculated measure for a rigid body that is undergoing rotational motion around a fixed axis: that is to say, it measures how difficult it would be to change an object’s current rotational speed.
What is the product of moment of inertia and angular acceleration?
torque
The torque on a given axis is given by the product of the moment of inertia and the angular acceleration. Thus, the product of moment of inertia and angular acceleration is torque.
How are torque and moment of inertia related?
When a torque is applied to an object it begins to rotate with an acceleration inversely proportional to its moment of inertia. This relation can be thought of as Newton’s Second Law for rotation. The moment of inertia is the rotational mass and the torque is rotational force.
Why is moment of inertia also called rotational inertia?
Moment of inertia is also called rotational inertia because it is a measure of the “resistence” of an object to be accelerated in its rotation. An object with a big moment of inertia is more difficult to increase/decrease its angular velocity (speed of rotation), than an object with a low moment of inertia.
What is moment of inertia in engineering mechanics?
moment of inertia in Mechanical Engineering The moment of inertia is a measure of how resistant an object is to changes in its rotational motion. The moment of inertia of the cross-section of a body is its resistance to changes in its rotation.