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## Mechanics.

During the years of the Plague Newton constructed what was to become an remarkably successful model of Nature. In it he proposed three laws that describe the motion of all material bodies (at least for all phenomena within reach at the time). These were not mere descriptions but actual calculational tools, and the enormous accuracy in the predictions achieved by this theory resulted in its universal acceptance that lasted more than two centuries...until Einstein came along.

After returning to Cambridge, Newton lost interest in mechanics until 1684. In this year Halley, tired of Hooke's boasting, asked Newton whether he could prove Hooke's conjecture that planets moved in ellipses because the sun attracted them with a force decreasing as the square of the distance. Newton told him that he had indeed solved this problem five years earlier, but had now mislaid the proof. At Halley's urging Newton reproduced the proofs and expanded them into a paper on the laws of motion and problems of orbital mechanics. Halley then persuaded Newton to write a full treatment of his new physics and its application to astronomy. Over a year later (in 1687) Newton published the Philosophiae Naturalis Principia Mathematica or the Principia as it is commonly known. It is one of the greatest scientific books ever written.

Newton laid in his Principia three laws which describe the motion of bodies. These laws have an immense range of applicability, failing only at very small distances (of 10 - 8 cm or less), for very strong gravitational fields (about 108 stronger than the Sun's), or for very large speeds (near 108 m/s).

The first of Newton's laws addresses the motion of free bodies. The second law states quantitatively how a motion differs form free motion. The third law states the effect experienced by a body when exerting a force on another object.

• 1st law. Every body continues its state of rest or uniform motion in a straight line unless it is compelled to change this state by forces acting on it.
• 2nd law. The effect of a force F on the motion of a body of mass m is given by the relation

F = m a

where a is the acceleration: a body in the presence of a force F attains an acceleration equal to F / m.

• 3rd law. Every body exerting a force on another, experiences a force exerted by the second body equal in magnitude and in opposite direction.

These three laws constitute Newton's basic hypothesis He asserted that they are valid in all circumstances and to all bodies, in particular for heavenly bodies as well as for earth objects; this marks the final passing of Aristotelian physics. All experimental evidence of the time (and for the next two centuries) was to support these hypothesis, Newton's theory became the theory of Nature.

I will now discuss some of the features of these laws.

Next: 1st Law and Newtonian Up: Isaac Newton Previous: Isaac Newton

Jose Wudka
9/24/1998