Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. The principle of inertia is one of the fundamental principles of
classical physics which are used to describe the
motion of
matter and how it is affected by applied
forces. Inertia comes from the Latin word,
iners, meaning idle, or lazy.
Isaac Newton defined inertia as his first law in his
Philosophiæ Naturalis Principia Mathematica, which states:
[1]
The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.
In common usage the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), or sometimes to its
momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his
First Law of Motion; that an object not subject to any net external force moves at a constant velocity. Thus an object will continue moving at its current
velocity until some force causes its speed or direction to change.
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Interpretations
Mass and inertia
Physics and
mathematics appear to be less inclined to use the popular concept of inertia as "a tendency to maintain momentum" and instead favor the mathematically useful definition of inertia as the measure of a body's resistance to changes in velocity or simply a body's inertial mass.
This was clear in the beginning of the 20th century, when the
theory of relativity was not yet created. Mass,
m, denoted something like an amount of substance or quantity of matter. And at the same time mass was the quantitative measure of inertia of a body.
The mass of a body determines the momentum
https://www.aulro.com/afvb/images/im...013/05/449.jpg of the body at given velocity
https://www.aulro.com/afvb/images/im...013/05/450.jpg; it is a proportionality factor in the formula:
https://www.aulro.com/afvb/images/im...013/05/451.jpg The factor
m is referred to as
inertial mass.
But mass, as related to the 'inertia' of a body, can also be defined by the formula:
https://www.aulro.com/afvb/images/im...013/05/452.jpg Here,
F is force,
m is mass, and
a is acceleration.
By this formula, the greater its mass, the less a body accelerates under given force. Masses
https://www.aulro.com/afvb/images/im...013/05/453.jpg defined by formula (1) and (2) are equal because formula (2) is a consequence of formula (1) if mass does not depend on time and velocity. Thus, "mass is the quantitative or numerical measure of body’s inertia, that is of its resistance to being accelerated".
This meaning of a
body's inertia therefore is altered from the popular meaning as "a tendency to maintain momentum" to a description of the measure of how difficult it is to change the velocity of a body. But it is consistent with the fact that motion in one reference frame can disappear in another, so it is the change in velocity that is important.
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