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Mechanics Notes

# Mechanics Notes - Lecture notes for Mechanics 1 Misha...

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Lecture notes for Mechanics 1 Misha Rudnev 1 On principles. Introduction If one studies natural phenomena, it is important to try to understand the underlying principles . These would ideally not only enable one to explain the range of familiar phenomena but may predict new phenomena or at least explain new phenomena when they are discovered. The method of principles was founded by Newton (1643–1727). Einstein (1879–1955) was a great master of the method of principles. Principles of physics are not a matter of logical explanation. Their confirmation is experience only – they are based on reality, or experimental facts which so far have had no evidence to the contrary. To this end, ”experiment” and ”reality” are herein tautological. Practically, however, these are not the principles themselves – as there aren’t so many – but their logical consequences that are observed in a vast variety of physical experiments and in general reality. Here are the examples of physical principles. The relativity principle – there are no observational consequences of absolute motion, see footnote 6 below, is a meta-principle which establishes a class of subjects, or observers, who are to embark on the study of natural phenomena and get the same results of identical independently performed physical experiments. These are closely related to Newton’s first law, the most philosophically mysterious one of three. See Section 3.2. Another meta-principle: physics works by way of fundamental constants (such as, say the mass of electron, the Gravitational constant, etc.) fundamental quantities (such as, say mass, energy, momentum) and laws, which can be expressed as the relations between these fundamental quantities and constant. Experience, or information that we possess is always limited, and so may be the scope of principles. Principles, discovered so far apply with limited precision only. Until now, the key trend in physics was expansion and extension of the principles’ scope. When new phenomena are discovered, it may happen that old principles cannot account for them and have to be abandoned or extended. Abandonment would indicate that the principles were somewhat false (although they may have used logically consistent mathematics). An ideal physicist is always in quest for an experiment that would invalidate his favorite theory. But even if this happens and the theory goes busted, yet the principles can be extended to embrace a new, more mature theory – this is hopefully an indication that one is on the right track. This happened in the beginning of the XX century when in order to apply classical Newtonian mechanics to the microworld on sub-atomic length scales ( . 10 - 8 cm) and, respectively, the fast world of speeds comparable with the speed of light in vacuum c 300 , 000 km/s, its principles had to be revised to embrace quantum mechanics and relativity theory. Throughout the revision some ideas and models that had outlived themselves, such as luminiferous ether 1 had to be dropped. New fundamental constants ( c , h

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