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# University Physics III PHYS 262

Mason

GPA 3.66

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This 17 page Study Guide was uploaded by Sonny Breitenberg on Monday September 28, 2015. The Study Guide belongs to PHYS 262 at George Mason University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/215194/phys-262-george-mason-university in Physics 2 at George Mason University.

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Date Created: 09/28/15

Inertial Reference Frames Inertial Reference Frames A coordinate system x yz I for labeling events attached to an observer who is not accelerating and there is noforce acting on it eg A space ship far away from any stars in deep space stopped or in constant velocity motion An effective Inertial Reference Frames Both S and S are not truly inertial ref frames because gravity acts on them But since g acts on them equally and is I to 11 their relative velocity we can treat them as e ecz ive inert ref frames Relative Motion S and S are in relative motion L A S would say that S moves to the right with respect to himher with speed u S would say that S moves to the left with respect to himher with same speed u it 39Q Galilean Relativity before Einstein Principle of Galilean Relativity The Laws ofMecham39cs must be the same in all inertial reference frames ie Newton s Laws of Motion apply equally to all inertial observers in relative motion with constant velocity Example observer in S throw a ball straight up L S Galilean Relativity before Einstein In S inertial ref frame Tj A i 3 Although the observed trajectories in S amp S are not the same the same Newton 5 Equation F 2 ma describes the observations in both situations In S inertial ref frame Ifquot 9H Galilean Coordinate Transformation How can one translate physical quantities from one inertial reference frame to another 3 V S 539 Frame 8 moves relative to J J I I x frame S With constant veloc1ty it along the common x xquot axis T K P an event y M Origins 0 and 0 0 i x 0 l r coincide at time r 0 zquot m Copyrigh 2003 Pearson Edunahon Inc publishing a5 Pearson Adaisnnrweilav u is the relative speed between S amp S Galilean Coordinate Transformation At a later time I xyzl amp x y Z l for event P are related by l w M Galilean spacetime 2355 transformation equations v Notice that in this classical Viewpoint so that clocks runs at the same rates in all inertial reference frames Galilean Velocity Transformation Let say there is a particle at point P moving in the xdirection with its instantaneous velocity vx as measured by an observer in S frame How is the velocity measured by an observer in S frame related to vx In S frame the particle moves a distance of clx in a time dl so that dx vx dz From the Galilean Coordinate Transformation we have in differential form dxdx39udt Galilean Velocity Transformation dx D1v1d1ng dz on both s1des of the equatlon glves u dt dt clx39 clx39 Since dz dl we have u u dt dt 611 g Galilean Velocity Transformation verso 0f relative velocity laealuellsb S between frames y velocity of particle as measured by S Ea The Constancy of the Speed of Light Recall the llIiclzelsonMorley experiment Similar to a boat light traveling in a owing river ether the speed of light was expected to depends on its relative motion with respect to the ether w 1mdhlunurrm39 u is the relative speed between the frames water amp shore Result Speed of light 0 does not follow the Galilean Velocity Transformation and c is the same for all inertial observers in relative motion The Constancy of the Speed of Light Recall om Maxwell s Equations in electromagnetic theory EM waves can be shown to travel according to the plane wave equation i 62EB 6x2 62 62 at the same speed c If we believe Maxwell s Equations to be correct in all inertial reference frames then we must accept that EM waves travel at the same speed c in all inertial reference frames Einstein s Postulates for Special Relativity 1 All laws of physics must be the same in all inertial reference frames Specific observations might be different but the same phenomena must be described by the same physical law Not just the laws of mechanics as in the Galilean Viewpoint All laws of physics include mechanics EM thermodynamics QM etc Same emf is induced in the coil 5 Einstein s Postulates 2 The speed of light 0 in vacuum is the same in all inertial reference frames and is independent of the observer or the source A missile M is fired with speed DM S 1000111 s relative in the spaceship a A spaceship 1539 moves WllI39l 1000 ms relative er on earth 5 spec to an obs Missile M gt UMSr 2000 ms UM 2000 mZS 1000 ms HEWTOHIAN MECHANICS HOLDS Newtonian mechanic39s tells us correctly that the missile moves with speed limp 3000 ms relative td the observer on earth 3 A Itght heam L Is emitted from the spaceship at speed i Light beam L 12575 10001115 Earth NEWTONIAN MECHANICS FAILS Newtonian mechanics tells us nht moves at a speed greater than t39 relative to the ich x ould contradict Einstein39s second postulate l Ls39 C 1000 ms ltt39m39ImIy thal the li observer on earth These two postulates form the basis of Einstein s Special Theory of Relativity Stating the Results First LS S multane ty Measured Measured TWO ashes by S by S simultaneous in S but not 1n S Length Con raction moving ruler get shorter l Notes on Relative Motion r a quot391quotquotI 39 1quotquot1 ash a flash b Both observers in S and S have their own measurement devices and they can also measure hisher partners devices and compare with hisher own Although time duration and length might depend on the observer s inertial frame they will agree on the following three items c is the same in all frames their relative speed u is the same all physical laws apply equally Relativity of Simultaneity Simultaneity azhalll ill 0 0 ash b De nition Two ashes event a and b are considered to be simultaneous with respect to observer 0 if light from a amp b equal distance to observer S in the middle arrive at the observer at the same time 95 Relativity of Simultaneity At time t 0 a LiUhtninU hits the front I Mav s I C c A 1 B and the back of a train H points A and B and l 39 i i S x hits the ground at points W H39 2 I J7 A and B 039 A B Q S Stanley 0 and O are respectively in the 0 middle of AB andA B We will analyze the situation in Stanley s S frame in the following slides Relativity of Sirnultaneity On the ground S frarne after some time t Inside the train Mavis moves 3 toward the light coming from the front of the train and away from the light coming from the S l back of the train 6 I 3 M0 Conyrlgm 2m Peavsnn Education Inc publishing a5 Pearson Adammwwey Light travels at the same speed c in both frames ll

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