Physics 325
Lecture 4
Frames of Reference
We referred above to an “inertial reference frame”.
What do we mean by this?
An inertial reference frame (IRF) is a reference frame that is not accelerating.
Not
accelerating with respect to what is a good question.
But it turns out that just saying it is
not accelerating is usually good enough – you can say “with respect to the fixed stars” if
you want to pretend that the stars are fixed.
A rotating reference frame is a counter example.
It is clearly an accelerating reference
frame since while rotating a body has centripetal acceleration.
So the earth is not really
an IRF, but we calculated our acceleration in Urbana in 111 and it’s pretty small, so it’s
approximately an IRF.
Newton’s laws are valid only in an IRF (though you can use them to derive laws in
NIRFs).
Furthermore, all IRFs are equivalent so we can derive a set of rules for moving
G
The rules that take us from
S
to
S’
are as follows:
from one frame
S
to another
S’
that moves with respect to
S
at a constant velocity
:
0
v
S
r
G
S’
r
′
G
0
constant
v
G
( )
( )
( )
( )
0
0
0
Therefore
r
t
r t
v t
′
=
−
G
G
G
d
d
r
t
r t
v
v
v
v
dt
dt
dv
dv
a
a
dt
dt
F
ma
F
ma
′
′
=
−
→
=
−
′
′
=
→
=
′
′
=
=
=
G
G
G
G
G
G
G
G
G
G
G
G
G
G
(4.1)
The last two equations in (4.1) show that Newton’s laws remain unchanged if we move
from one IRF to another.
This is known as Galilean invariance, and it is due to the fact
that Newton’s 2
nd
law involves a derivative of the velocity, so addition of a constant
velocity drops out.

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