S2.1 Inertial reference frames: Newton`s 1st Law
Preamble
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Preamble
- The pre-Newtonian question:
What sustains an object’s velocity?
- The post-Newtonian question:
What controls an object’s acceleration?
- The qualitative answers:
the external influence it feels
– we call this force
its inertia (resistance) against acceleration
—we call this mass
- the reference frame from which it is viewed
- Empirically, we find that a block sliding on a table has constant velocity if
- the surface is made smooth enough
- we view it from the earth’s reference frame
- This kind of observation is generalised to give Newton’s 1st Law.
Key Point 2.1
Newton’s 1st Law. A body free of external ‘influences’ will have constant velocity (zero acceleration) with respect to any inertial reference frame.
About ‘influences’
You would instinctively write ‘forces’ instead of ‘influences’. But we haven’t yet got round to defining what we mean by a force. So we shouldn’t use that term yet. We assume that we can all agree on what is meant by ‘influence’ (though it’s not a very scientific word). Once we have got round to defining a ‘force’ you can come back here, score out ‘influences’ and write ‘forces’ instead. Some of you will wish we just wrote it that way from the start...This statement defines the term inertial reference frame
– an inertial reference frame is one in which the 1st Law holds!
A remote star is an ideal inertial frame
– because it is itself ‘free of external influences’.
- Any reference frame moving at constant velocity w.r.t. an
inertial frame is also inertial
– the Galilean transformations (Key Point 1.9)
guarantee this.
Help?
Consider a body P that is ‘free from external influences’. And suppose that frame A is ‘inertial’. Then P will move uniformly (ie at constant velocity) with respect to A so that
.
Now if frame B is moving uniformly with respect to frame A (so that
) then the Galilean transformations tell us that
also. So P moves uniformly with respect to B...and B is an inertial frame too.
- The earth is approximately
an inertial frame.
Learning Resources
![]() | HRW Chapter 5.1-3 |