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Reference Frame First Law Newton’s first law says that with no net force there is no acceleration. • Objects at rest • Objects at constant velocity If there is no observed acceleration on an object with no net force, the observer is in an inertial reference frame. • Newton’s laws of mechanics apply equally • No absolute motion Inertial Frame An observer on the table sees two ball fall. • First straight down • Second in a parabola An observer with speed vx0 sees the reverse. • Second straight down • First in a backwards parabola Both frames are inertial. • Motion consistent with Newton Accelerated Frame A rotating observer throws a ball across a merry-go-round. • Ball veers to the side • No external force This is a non-inertial frame. • Observed motion inconsistent with Newton’s laws • Fictitious forces Galilean Relativity An event is a point in space y y’ S S’ v and time. • Described by coordinates: (x, y, z, t) x’ A different frame of reference x uses different coordinates. The Galilean transformation converts between two inertial frames. • Coincide at t = 0 Event P x x x vt y y z z t t x’ Relative Velocity The Galilean transformation y y’ S provides a conversion for relative velocity. P • Moving event P • Observed velocity u, u’ x ux u x v uy u y uz uz v S’ u’ u x’ Moving Light Light as a wave should have a medium for transmission. ether • Like a plane in the wind • Speed in ether c light observed The ether velocity and the light velocity must add to get the result from the earth. u c 2 v 2 Universal Constant Maxwell’s equations assume a constant value for c. • Independent of motion • Independent of observer Mechanical waves should follow Galilean relativity. • Speed depends on observer’s relative motion This was the paradox of the “ether”. • Newton and Maxwell contradict next