Moment of Inertia | B.Sc 1st Semester | Moment of Inertia in Hindi | Newtonian Mechanics | NEP 2020

The moment of inertia, often denoted by 𝐼, is a fundamental concept in rotational dynamics, analogous to mass in linear motion. It measures an object's resistance to changes in its rotational motion around a specific axis. Essentially, it tells us how difficult it is to rotate an object about that axis.

Definition: The moment of inertia of a body is the sum of the products of the mass elements of the body and the square of their distances from the axis of rotation. Mathematically, for a continuous body

Moment of Inertia of Symmetric I-Section || Strength of Materials ||
The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis.

For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other

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