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happyphysics.com Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com

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Ch 37 Relativity © 2005 Pearson Education

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37.1 Invariance of Physical Laws © 2005 Pearson Education Same emf induced

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Einsteins Postulate First Postulate: The laws of physics are the same in every inertial frame of reference. First Postulate: The laws of physics are the same in every inertial frame of reference. Second Postulate: The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source. Second Postulate: The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source. © 2005 Pearson Education

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Galilean coordinate transformation

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Galilean velocity transformation © 2005 Pearson Education

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37.2 relativity of Simultaneity © 2005 Pearson Education

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Whether or not two events at different x-axis locations are simultaneous depends on the state of motion of the observer

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37.3 Relativity of Time Intervals © 2005 Pearson Education At rest: t 0=2d/c

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During time t © 2005 Pearson Education

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time dilation © 2005 Pearson Education

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Example 37.1 High-energy subatomic particles coming from space interact with atoms in the earth s upper atmosphere, producing unstable particles called muons. A muon decays with a mean lifetime of 2.2*10 -6 s as measured in a frame of reference in which it is at rest. If a muon is moving at 0.99c relative to the earth, what will you measure its mea lifetime to be? ANS: © 2005 Pearson Education

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37.4 Relativity of Length length contraction © 2005 Pearson Education

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Example 37.4 A spaceship flies past earth at a speed of 0.99c. A crew member on board the spaceship measures its length, obtaining the value 400m. What length do observers measure on earth? A spaceship flies past earth at a speed of 0.99c. A crew member on board the spaceship measures its length, obtaining the value 400m. What length do observers measure on earth?ANS: © 2005 Pearson Education

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37.5 The Lorentz Transformations © 2005 Pearson Education

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Lorentz coordinate transformation Lorentz velocity transformation © 2005 Pearson Education

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37.6 the Doppler Effect for Electromagnetic Waves Doppler effect, electromagnetic waves © 2005 Pearson Education

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relativistic momentum 37.7 Relativistic Momentum © 2005 Pearson Education

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37.8 Relativistic Work and Energy © 2005 Pearson Education

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relativistic kinetic energy total energy, rest energy, and momentum © 2005 Pearson Education

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37.9 Newtonian Mechanics and Relativity © 2005 Pearson Education

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All of the fundamental laws of physics have the same form in all inertial frames of reference. The speed of light in vacuum is the same in all inertial frames and is independent of the motion of the source. Simultaneity is not an absolute concept; events that are simultaneous in one frame are not necessarily simultaneous in a second frame moving relative to the first.

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If two events occur at the same space point in a particular frame of reference, the time interval t 0 between the events as measured in that frame is called a proper time interval. If this frame moves with constant velocity u relative to a second frame, the time interval t between the events as observed in the second frame is longer than t 0. This effect is called time dilation. (Examples 37.1 through 37.3) © 2005 Pearson Education

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If two points are at rest in a particular frame of reference, the distance l 0 between the points as measured in that frame is called a proper length. If this frame moves with constant velocity u relative to a second frame and the distances are measured parallel to the motion, the distance l between the points as measured in the second frame is shorter than l 0. This effect is called length contraction. (See Examples 37.4 through 37.6) © 2005 Pearson Education

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The Lorentz coordinate transformation relates the coordinate and time of an event in an inertial frame S to the coordinates and time of the same event as observed in a second inertial frame S moving at velocity u relative to the first. For one-dimensional motion, a particles velocities v x in S and v x in S are related by the Lorentz velocity transformation. (See Examples 37.7 and 37.8) © 2005 Pearson Education

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The Doppler effect is the frequency shift in light from a source due to the relative motion of source and observer. For a source moving toward the observer with speed u, Eq.(37.25) gives the received frequency f in terms of the emitted frequency f 0.(See Example 37.9)

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For a particle of rest mass m moving with velocity, the relativistic momentum is given by Eq. (37.27) or (37.31) and the relativistic kinetic energy K is given by Eq. (37.36). The total energy E is the sum of the kinetic energy and the rest energy mc 2. The total energy can also be expressed in terms of the magnitude of momentum p and rest mass m. (See Examples through 37.12) © 2005 Pearson Education

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The special theory of relativity is a generalization of Newtonian mechanics. All the principles of Newtonian mechanics are present as limiting cases when all the speeds are small compared to c. Further generalization to include noninertial frames of reference and their relation to gravitational fields leads to the general theory of relativity.

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