introduction to classical mechanics by takwale pdf download
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In the middle of the nineteenth century, classical mechanics suddenly seemed to be getting nowhere. One of its principles was that 'every body perseveres in its state of rest or uniform motion in a straight line', but many physicists noticed that this rule seemed to break down when Newton's laws were applied to objects undergoing acceleration. Instead of becoming more and more uniform as predicted, a body would change shape as it accelerated, and some would even move backwards. This data led to a new field of physics which came to be known as 'special relativity'. Classical mechanics still had its uses however. It provided us with our first evidence-based understanding about how batteries work and it even helped create quantum mechanics. But the key to unlocking the mysteries of special relativity is classical mechanics. Special relativity was created by inventing a new set of rules for when objects change speed - in addition to when they don't. The equations for forces, forces' acceleration and the net result of all the forces were all wrong, so Newton's law had to be scrapped in favor of 'Newton's third law': "every action has an opposite and equal reaction". The Lorentz transformations are tools for describing how time, space and motion are interrelated. They are based on mathematics that obey what is known as Galilean invariance, which states that no force or effect can travel at the same speed as light. However, it is not known whether this equivalence is compatible with relativity. The Lorentz transformations are three equations that transform three quantities in space, time and momentum in spacetime into their components in space and time. According to special relativity these equations are valid only for the accelerated frame of reference moving with constant speed. These transformations are mathematically defined by the Lorentz transformation which transforms three quantities of the three dimensional object formula_1 by the following equations for all observer formulas_2: where formula_4 is velocity / distance"t"; formula_5 is velocity / time"x"; formula_6 is force/mass"M"; formula_7 is momentum "p"; and formula_8. The formula_9 factor is the speed of light "c". In these equations, formula_10 and formula_11 are speed and length of the object (and frame) respectively. As such, the relativistic transformation between time and length is expressed in these equations. If we let P be a position vector in 4-dimensional space-time, we can write P as: For 3D space: P = [x(t), y(t), z(t)] and for 1D spacetime: P = [x(t), y(t), t] . The Lorentz factor then becomes: As shown by Maxwell's equations, electromagnetic waves propagate at velocity c relative to their source. If the speed of light is finite, then according to special relativity, all electromagnetic waves propagate at the speed of light. Under this assumption, the time dilation factor becomes: As for electromagnetism, forces are also instantaneous in nature. According to special relativity, there are no forces before an object comes into contact with another object. An example of this is Isaac Newton's Third Law. According to this law, force has an equal and opposite reaction . This means that if you push an object with a force parallel to it's acceleration vector, there would be an equal and opposite force pushing back on you pushing you in the other direction causing your body to accelerate.

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