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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. (This is called Newton's first law of motion, taken from Galileo's principle.) The term is also used in psychology to describe a person's resistance to change.
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, in the Aristotelian view, a projectile moving through the air would owe 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.
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 the property which maintained the motion also 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 would be arrested by the forces of air resistance and gravity which might be opposing its impetus. Buridan further held that the impetus of a body increased with the speed with which it was set in motion, and with its quantity of matter. Clearly, Buridan's impetus is closely related to the modern concept of momentum. Buridan anticipated Isaac Newton when he wrote:
- ...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 Aristotelian 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.
In the summer of 1954, a student and future Nobel Prize winner observed a reproducible perturbation of the laws of inertia and Einstein's "Theory of Relativity" associated with the alignment of the earth, moon, and sun during an eclipse. Maurice Allais' observations have since been reproduced with enough confidence to satisfy some scientists.
Newton adopted Galileo's principle as his first law of motion and set it within the wider context of what came to be known as Newtonian physics. In Newton's theory, no force is required to maintain a body in uniform motion, in contrast to Aristotle's view, where no force is needed to maintain a body 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, a linear, sliding translation at constant velocity) to convert their observations for another's observations. 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, which is moving at a constant velocity, the ball also has an inertia in the direction of travel that maintains its relative position, with respect to the moving train, when the ball is dropped.
However, in non-inertial frames, accelerating observers encounter all sorts of fictitious forces, such as the Coriolis force, that would not be experienced in an inertial frame of reference (such as the frame of the "fixed stars" like Polaris).
In summary, the principle of inertia is intimately linked with the principles of conservation of energy and conservation of momentum. Thus a change in momentum or energy would have to be applied to the observer or to the system in a conversion of the viewpoint from an inertial frame to some non-inertial frame.
The equivalence of mass and inertia seems to hold true according to all empirical evidence (see gravitational physics and also Mach's principle, below). In theory at least they are sometimes regarded as being separate qualities.
Mach's principle deals with the question of the origin of inertia. Therefore it deals only with accelerated motion, not with uniform motion. Mach had stated that the absolute space that is assumed in newtonian dynamics is unsatisfactory in a philosophy of physics that demands that all dynamics is to be explained in terms of interactions of material objects. If there is absolute space then in a universe with just a single object in it that object will have inertia. A mass of water will contract itself to a sphere of water, and if this mass of water is spinning then it wil not be spherical in shape, but the shape will be an ellipsoid, due to inertia. In order to formulate a theory in which there is no necessity of assuming absolute space, it would have to be a theory in which the existence of inertia is due to an interaction of local matter with distant matter, a theory in which the existence of inertia is due to interaction of local matter with all of the matter in the universe. Albert Einstein named this Mach's principle.
In Newton's judgement, assuming absolute space was an unavoidable necessity. The alternative would be to assume an action at a distance from the stars, and Newton was committed to avoiding assumptions of action-at-a-distance whenever possible. Newton needed absolute space for accelerated motion only; only with absolute space would water rotating in a bucket "know" what concave shape to take. However, for uniform motion newtonian dynamics implies that in all inertial reference frames the same laws of motion apply: the principle of Galilean relativity. Special relativity was a reassertion of this type of relativity: in all inertial reference frames the same laws of physics hold.
In general relativity the description of gravity and the description of inertia are unified. Both are described as interaction of matter with the geometry of space-time. A force opposing gravity is described as the same physics as a force that is accelerating an object: both are described as an interaction with a gravito-inertial field. The gravito-inertial field exists because the universe exists. In general relativity the action at a distance is mediated by space-time geometry.
Mach's original thought was to eliminate space altogether as a agent in physics. Newtonian absolute space acts on matter but is not acted upon by matter, that was very unsatisfactory. Einstein did the opposite of what Mach had envisioned, in general relativity space-time geometry is described as part of the realm of physical things. In general relativity space-time acts upon matter and it is acted upon by matter.
"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 (involving the second derivative of displacement) and some restoring force (involving the zeroth derivative of displacement) that allows a system to oscillate.
- In these systems, the multiplier of the second derivative term plays a role analogous to mass in a mechanical system: in particular, inductance in loaded electrical systems and inertance in acoustical systems.
- Importantly, there is no thermal analogue of inertia entailing that there are no un-driven thermal oscillations.
A further analogy is that of rotational inertia in which a rotating body maintains its state of uniform rotational motion. Thus its angular momentum would be unchanged, unless an external torque were to be applied. Rotational inertia often has hidden practical consequences. In the braking of a railway train, arresting the linear motion would require that the substantial rotational inertia of the motors must be converted to some other forms of energy, thus causing acoustic vibration of the wheels and frictional heating of the brakes on the railway carriage.
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.
Books and papers
- Butterfield, H (1957) The Origins of Modern Science ISBN 071350160X
- Clement, J (1982) "Students' preconceptions in introductory mechanics", American Journal of Physics vol 50, pp66-71
- Crombie, A C (1959) Medieval and Early Modern Science, vol 2
- McCloskey, M (1983) "Intuitive physics", Scientific American, April, pp114-123
- McCloskey, M & Carmazza, A (1980) "Curvilinear motion in the absence of external forces: naÔve beliefs about the motion of objects", Science vol 210, pp1139-1141
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