Reference Frame

First Law  Newton’s first law says that with no net force there is no acceleration. Objects at restObjects at rest Objects at constant velocityObjects 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 equallyNewton’s laws of mechanics apply equally No absolute motionNo absolute motion

Inertial Frame  An observer on the table sees two ball fall. First straight down Second in a parabola  An observer with speed v x0 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 and time. Described by coordinates: ( x, y, z, t )Described by coordinates: ( x, y, z, t )  A different frame of reference uses different coordinates.  The Galilean transformation converts between two inertial frames. Coincide at t = 0Coincide at t = 0 y x Sy’ x’ S’ Event P x x’ v

Relative Velocity  The Galilean transformation provides a conversion for relative velocity. Moving event PMoving event P Observed velocity u, u’Observed velocity u, u’ y x Sy’ x’ S’ P u u’ v

Moving Light  Light as a wave should have a medium for transmission. Like a plane in the wind Speed in ether c  The ether velocity and the light velocity must add to get the result from the earth. observed light ether

Universal Constant  Maxwell’s equations assume a constant value for c. Independent of motionIndependent of motion Independent of observerIndependent of observer  Mechanical waves should follow Galilean relativity. Speed depends on observer’s relative motionSpeed depends on observer’s relative motion  This was the paradox of the “ether”. Newton and Maxwell contradictNewton and Maxwell contradict next