Inertia

In physics, inertia is an historical concept and a perceived property of matter that exhibited an 'apparent' resistance to change of motion. It is now known that 'inertia' actually solely relates to the conservation of linear momentum or the conservation of angular momentum of a rotating object and describes how much force or torque is needed to accelerate the object at a given rate. The 'motion-maintaining' property is now realised not to exist and the reality of the situation is as stated by Newton's first law.

History

The tendency of a body to maintain its state of uniform motion unless acted on by an external unbalanced force is called Newton's first law of motion, taken from Galileo's principle.) This tendency is sometimes referred to as 'inertia' although this term has no real scientific meaning distinct from mass (for linear motion) and moment of inertia (for rotational motion).

The concept of inertia was 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 almost 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 Averroës 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. There is an important difference between our modern concept of momentum and Buridan's concept of impetus. Buridan saw impetus as causing the motion of the object, whereas momentum is a property caused by motion. 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.

Newtonian mechanics

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 nor is a force required to maintain it at rest. The tendency for objects to remain stationary or to continue to move at a constant speed was labeled inertia. But according to Newtons law, there was no necessity to introduce the concept of inertia. This is in contrast to Aristotle's view, where a force was thought to be needed to maintain a body in constant motion.

The mass of an object determines the rate at which it will accelerate linearly for a given force (Newton's Second Law of Motion). Similarly, the combination of the mass of an object and the distance of that mass from the axis of rotation (collectively called the moment of inertia) determines the rate at which it's rotation will accelerate for a given torque. Consequently more massive objects require larger forces to accelerate (or decelerate) them and appear to exhibit more inertia.

'Inertial' frames

In a location such as a steadily moving railway carriage, a dropped ball would behave as it would if it were dropped in a stationary carriage. The ball would simply descend vertically. It is possible to ignore the motion of the carriage by defining it as an inertial frame. In a moving but non-accelerating frame, the ball behaves normally because the train and its contents continue to move at a constant velocity. Before being dropped, the ball was traveling with the train at the same speed and the ball's inertia ensured that it continued to move in the same speed and direction as the train, even while dropping.

In an inertial frame all the observers in uniform (non-accelerating) motion will observe the same laws of physics. However observers in another inertial frames can make a simple, and intuitively obvious, transformation (the Galilean transformation), to convert their observations. Thus, an observer from outside the moving train could deduce that the dropped ball within the carriage fell vertically downwards.

However, in frames which are experiencing acceleration (non-inertial frames), objects appear to be affected by fictitious forces. For example, if the railway carriage was accelerating, the ball would not fall vertically within the carriage but would appear to an observer to be deflected because the carriage and the ball would not be traveling at the same speed while the ball was falling. Other examples of fictitious forces occur in rotating frames such as the earth. For example, a missile at the North Pole could be aimed directly at a location and fired southwards. An observer would see it apparently deflected away from its target by a force (the Coriolis force) but in reality the southerly target has moved because earth has rotated while the missile is in flight. Because the earth is rotating a useful inertial frame of reference is defined by the stars, which only move imperceptibly during most observations.

In summary, the principle of inertia is intimately linked with the principles of conservation of energy and conservation of momentum.

Rotational inertia

A further analogy is that of rotational inertia in which a rotating body maintains its state of uniform rotational motion due to conservation of angular momentum. Thus its angular momentum is unchanged, unless an external torque were to be applied. Rotational inertia often has hidden practical consequences. The somewhat inaccurate term moment of inertia is still used to describe the conservation of angular momentum for a rotating body.

External links

• Jean Buridan Stanford Encyclopaedia of Philosophy

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: naïve beliefs about the motion of objects", Science vol 210, pp1139-1141
• http://arxiv.org/abs/physics/0211106 UNIVERSALITY Emil Marinchev, Technical University of Sofia, Physics Department, 8 Kliment Ohridski St., Sofia-1000, BG, e-mail: [email protected] Abstract: This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws. A new theoretical scheme is proposed based on two basic principles: 1.The principle of universality of the conservation laws, and 2.The principle of the universal velocity. It is well- founded with examples of different fields of physics. Comments: 5 pages, 1 figure, Subj-class: General Physics, Key words:Universality, New Insight in Physics http://arxiv.org/abs/physics/0211106