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Lect24 - Relativity Chapter 27(1 of 2 Galilean classical...

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11/29/11 1 Relativity Galilean, classical Relativity Time dilatation Simultaneity Length contraction Addition of velocities Momentum Mass and energy General relativity Physics 104, Fall 2011 1 Physics 104 Lecture 23 Nov. 28, 2011 Chapter 27 (1 of 2) 11/29/11 Galilean Relativity Choose a frame of reference Necessary to describe a physical event According to Galilean Relativity, the laws of mechanics are the same in all inertial frames of reference An inertial frame of reference is one in which Newton’s Laws are valid Inertial references in a state of constant, rectilinear motion with respect to each other they are not accelerated (carousel cabin, accelerating elevator) Objects subjected to no forces will move in straight lines November 11 Physics 104, Fall 2011 2
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11/29/11 2 Relativity The term relativity arises when a situation is described from two different points of view When the railroad car moves with a constant velocity, Ted and Alice see different motions of the ball Relativity Ted observes the ball’s motion purely along the vertical direction Ted would think the ball’s horizontal velocity is zero, but Alice would disagree Alice sees the ball undergo projectile motion with a nonzero displacement in both the x- and y-directions
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11/29/11 3 Galilean Relativity – Example 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 Conclusion: There is no preferred frame of reference for describing the laws of mechanics November 11 Physics 104, Fall 2011 5 Addition of Velocities Non-relativistic Velocities can simply be added. If in more than one dimension, use vector addition. November 11 Physics 104, Fall 2011 6
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11/29/11 4 Relative Velocity (Ball) Your friend throws a ball at 20 mph towards you. How fast do you think it moves when you are: – Standing still – Running 10 mph towards – Running 10 mph away November 11 Physics 104, Fall 2011 7 20 mph 30 mph 10 mph Addition of velocities November 11 Physics 104, Fall 2011 8 Your friend fires a laser at you while you're standing still. You measure the photons to be coming towards you at the speed of light (c = 3.0 x 10 8 m/s) . You start running away from your friend at half the speed of light (c/2 = 1.5 x 10 8 m/s) . Now how fast do you measure the photons to be moving?
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