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Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics , and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [ 1 ]
An arbitrary object's moment of inertia thus depends on the spatial distribution of its mass. In general, given an object of mass m , an effective radius k can be defined, dependent on a particular axis of rotation, with such a value that its moment of inertia around the axis is I = m k 2 , {\displaystyle I=mk^{2},} where k is known as the ...
Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration). The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2).
In such a frame, the interactions between physical objects vary depending on the acceleration of that frame with respect to an inertial frame. Viewed from the perspective of classical mechanics and special relativity, the usual physical forces caused by the interaction of objects have to be supplemented by fictitious forces caused by inertia.
Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon. [note 3] Newton's first law expresses the principle of inertia: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the ...
In physics, moment of inertia is strictly the second moment of mass with respect to distance from an axis: =, where r is the distance to some potential rotation axis, and the integral is over all the infinitesimal elements of mass, dm, in a three-dimensional space occupied by an object Q. The MOI, in this sense, is the analog of mass for ...
Angular momenta of a classical object. Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r ...
The second polar moment of area, also known (incorrectly, colloquially) as "polar moment of inertia" or even "moment of inertia", is a quantity used to describe resistance to torsional deformation (), in objects (or segments of an object) with an invariant cross-section and no significant warping or out-of-plane deformation. [1]