chapter9_1 - Chapter 9 Relativity Basic Problems Newtonian...

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Chapter 9 Relativity
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Basic Problems ± Newtonian mechanics fails to describe properly the motion of objects whose speeds approach that of light ± Newtonian mechanics is a limited theory ± It places no upper limit on speed ± It is contrary to modern experimental results ± Newtonian mechanics becomes a specialized case of Einstein’s special theory of relativity ± When speeds are much less than the speed of light
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Newtonian Relativity ± Inertial frames of reference ± Objects subjected to no forces will experience no acceleration ± Any system moving at constant velocity with respect to an inertial frame must also be in an inertial frame ± According to the principle of Newtonian relativity , the laws of mechanics are the same in all inertial frames of reference
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Newtonian Relativity – Example ± The observer in the truck throws a ball straight up ± It appears to move in a vertical path ± The law of gravity and equations of motion under uniform acceleration are obeyed
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Newtonian Relativity – Example, cont. ± There is a stationary observer on the ground ± Views the path of the ball thrown to be a parabola ± The ball has a velocity to the right equal to the velocity of the truck
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Newtonian Relativity – Example, conclusion ± The two observers disagree on the shape of the ball’s path ± Both agree that the motion obeys the law of gravity and Newton’s laws of motion ± Both agree on how long the ball was in the air ± All differences between the two views stem from the relative motion of one frame with respect to the other
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Views of an Event ± An event is some physical phenomenon ± Assume the event occurs and is observed by an observer at rest in an inertial reference frame ± The event’s location and time can be specified by the coordinates ( x , y , z , t )
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Views of an Event, cont. ± Consider two inertial frames, S and S’ ± S’ moves with constant velocity, , along the common x and x ’axes ± The velocity is measured relative to S ± Assume the origins of S and S’ coincide at t = 0
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Galilean Transformation of Coordinates ± An observer in S describes the event with space-time coordinates ( x , y , z , t ) ± An observer in S’ describes the same event with space-time coordinates ( x ’, y ’, z ’, t ’) ± The relationship among the coordinates are ± x ’= x vt ± y ’= y ± z ’= z ± t ’= t
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Notes About Galilean Transformation Equations ± The time is the same in both inertial frames ± Within the framework of classical mechanics, all clocks run at the same rate ± The time at which an event occurs for an observer in S is the same as the time for the same event in S’ ± This turns out to be incorrect when v is comparable to the speed of light
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Galilean Transformation of Velocity ± Suppose that a particle moves through a displacement dx along the x axis in a time dt ± The corresponding displacement dx ’is ± u is used for the particle velocity and v is used for the relative velocity between the two frames
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chapter9_1 - Chapter 9 Relativity Basic Problems Newtonian...

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