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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
ux  u x  v
uy  u y
uz  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
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