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Inertia
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Inertia

Inertia is the tendency of any state of affairs to persist in the absence of external influences. Specifically, in physics, it is the tendency of a body to maintain its state of uniform motion unless acted on by an external force.

Table of contents
1 History
2 Newtonian mechanics
3 Measuring Inertia
4 Mach's principle
5 "Inertia" in non-mechanical systems
6 Rotary inertia
7 Intuitive physics
8 See also
9 External links
10 Books and papers

History

The concept of inertia is alien to the physics of Aristotle which provided the standard account of motion until the 17th century. Aristotle, and his peripatetic followers, held that a body was only maintained in motion by the action of a continuous external force. Thus, a projectile moving through the air owed its continuing motion to eddies or vibrations in the surrounding medium, a phenomenon known as antiperistasis. In the absence of a proximate force, the body would come to rest immediately.

In the 6th century, Joannes Philoponus first criticised Aristotle's notion and proposed that motion was maintained by some property of the body, imparted when it was set in motion.

This view was strongly opposed by AverroŽs and the scholastic philosophers who supported Aristotle. William of Occam argued forcibly for Philoponus's theory but supporters still held the view that whatever property maintained the motion dissipated as it moved.

In the 14th century, Jean Buridan named the motion-maintaining property impetus and rejected the view that it dissipated spontaneously, asserting that a body is arrested by the foces of air resistance and gravity opposing its impetus. Buridan further held that the impetus of a body increases with the speed with which it is set in motion and with its quantity of matter. Clearly, Buridan's impetus is closely related to the modern concept of momentum and he anticipates Isaac Newton when he writes:

...after leaving the arm of the thrower, the projectile would be moved by an impetus given to it by the thrower and would continue to be moved as long as the impetus remained stronger than the resistance, and would be of infinite duration were it not diminished and corrupted by a contrary force resisting it or by something inclining it to a contrary motion

Buridan used the theory of impetus to give an accurate qualitative account of the motion of projectiles but he ultimately saw his theory as a correction to Aristotle, maintaining core peripatetic beliefs including a fundamental qualitative difference between motion and rest.

The theory of impetus was adapted to explain celestial phenomena in terms of circular impetus. Leonardo da Vinci, mistakenly, wrote Everything moveable thrown with fury through the air continues the motion of its mover; if, therefore, the latter move in a circle and release it in the course of this motion, its movement will be curved.

Sometime between 1589 and 1592, Galileo Galilei started researching the motion of moving bodies using the impetus theory of Hipparchus. Following an audacious series of experiments, both in practice and in thought, Galileo came to reject the Aristotlean view and to formulate a new principle of inertia, sometimes known as Galileo's principle:

Every object persists in its state of rest, or uniform motion (in a straight line); unless, it is compelled to change that state, by forces impressed on it.

Newtonian mechanics

Isaac Newton adopted Galileo's principle as his first law of motion and set it within the wider context of what is known as Newtonian physics. In Newton's theory, no force is required to maintain a body in uniform motion, just as, in Aristotle, none is needed to maintain it at rest. The impetus of a body was the cause of motion but its Newtonian equivalent, momentum is simply descriptive, no cause being required.

The loss of the ontological distinction between rest and motion leads to the concept of inertial frames which demand that observers in uniform (non-accelerating) motion all observe the same laws of physics. Observers in distinct inertial frames can make a very simple, and intuitively obvious, transformation (the Galilean transformation) to convert their observations for each other. Thus, an observer on a moving train sees a dropped ball fall vertically downwards as does an observer of a similar ball in a stationary frame. The relationship holds because, on the train, the ball has an inertia in the direction of travel that maintains its relative position, with respect to the train, when dropped.

Accelerating observers encounter all sorts of fictitious forces, such as the Coriolis force, that are simply not experienced in an inertial frame.

The principle of inertia is intimately linked with the principles of conservation of energy and conservation of momentum.

Measuring Inertia

The unit of measure for Inertia is the same as for mass. Typically it is expressed in grams or kilograms.

The equivalence of mass and intertia seems to hold true according to all empirical evidence. In theory at least they are sometimes regarded as being separate qualities.

Mach's principle

In the 18th century, English philosopher George Berkeley proposed that motion should be categorised as uniform or non-uniform against a frame fixed with respect to the distant stars. Independently, in 1893, Ernst Mach, motivated by his phenomenalist philosophy, proposed the principle that:

The inertia of any system is the result of the interaction of that system and the rest of the universe. In other words, every particle in the universe ultimately has an effect on every other particle.

Albert Einstein named this Mach's principle and was attracted to its suggestion that there was no need of an absolute, unique or special frame of reference against which claims of rest or motion would be judged. Though Galileo and Newton had apparently eliminated the distinction in the 17th century, by the late 19th century it had re-asserted itself in the form of the luminiferous aether, a mysterious medium conjured to support the new discoveries in electromagnetism. Einstein drew on Mach's principle in his original development of special relativity but later abandoned it as unnecessary. Einstein fiercely re-asserted the equivalence of all inertial frames and showed that, once combined with the principle of the constancy of the speed of light, it led to satisfactory explanations of many surprising physical phenomena.

"Inertia" in non-mechanical systems

In mathematical descriptions of mechanical systems, the mass of a body appears in a term featuring the acceleration, the second derivative of displacement; as, for example, in the harmonic oscillator. It is this term that provides the dynamics of the system in that, if we vary the system slowly enough we can make the term small and the system behaves quasi-statically. It is the interaction between the inertial term and some restoring force that allows a system to oscillate.

However, other physical phenomena exhibit similar behaviour and are described by second-order differential equations. In these systems, the multiplier of the second derivative plays a role analogous to mass in a mechanical system: in particular, inductance in electrical systems and inertance in acoustical. Importantly, there is no thermal analogue of inertia entailing that there are no un-driven thermal oscillations.

Rotary inertia

A further analogy is that of rotary inertia in which a rotating body maintains its state of uniform rotation, or remains free of angular momentum, unless an external torque is applied. Rotary inertia often has hidden practical consequences. In the braking of a railway train, arresting the linear motion requires that the substantial rotary inertia of the motors must be converted to some other form of energy.

Intuitive physics

Commonly, when people unschooled in Newtonian physics are asked to make predictions about certain sorts of motions involving inertia, their responses are more likely to reflect the theories of Aristotle than of Newton.

See also

Energy | General relativity | Inertial frame | Inertial guidance system | Inertial mass | Mach's principle | Momentum | Newton's laws of motion | Newtonian physics | Special relativity

External links

Books and papers