Notes on Relativity and Cosmology - Physics Department, UCSB

1.6. HOW CAN YOU TELL IF AN OBJECT IS IN AN INERTIAL FRAME?35
However, one of the discoveries of Newtonian Physics was that not all reference
frames are in fact equivalent. There is a special set of reference frames that
are called Inertial Frames. This concept will be extremely important for us
throughout the course.
Here’s the idea:
Before Einstein, physicists believed that the behavior of almost everything
(baseballs, ice skaters, rockets, planets, gyroscopes, bridges, arms, legs, cells,
...) was governed by three rules called ‘Newton’s Laws of Motion.’ The basic
point was to relate the motion of objects to the ‘forces’ that act on that object.
These laws picked out certain reference frames as special.
The first law has to do with what happens when there are no forces. Consider
someone in the middle of a perfectly smooth, slippery ice rink. An isolated
object in the middle of a slippery ice rink experiences zero force in the horizontal
direction. Now, what will happen to such a person? What if they are moving?
Newton’s first law of motion:
There exists a class of reference frames (called inertial frames) in which an
object moves in a straight line at constant speed (at time t) if and only if zero
(net) force acts on that object at time t.
⋆⋆ Note: When physicists speak about velocity this includes both the speed
and the direction of motion. So, we can restate this as: There exists a class of
reference frames (called inertial frames) in which the velocity of any object is
constant (at time t) if and only if zero net force acts on that object at time t.
⋆ ⋆ ⋆ This is really an operational definition for an inertial frame. Any frame in
which the above is true is called inertial.
⋆ The qualifier ‘net’ (in ‘net force’ above) means that there might be two or
more forces acting on the object, but that they all counteract each other and
cancel out. An object experiencing zero net force behaves identically to one
experiencing no forces at all.
We can restate Newton’s first law as:
Object A moves at constant velocity in an inertial frame ⇔ Object A
experiences zero net force.
Here the symbol (⇔) means ‘is equivalent to the statement that.’ Trust me, it
is good to encapsulate this awkward statement in a single symbol.
1.6 How can you tell if an object is in an inertial
frame?
Recall Newton’s first Law: There exists a class of reference frames (called inertial
frames). If object A’s frame is inertial, then object A will measure object B to