S1.5 Relativity: the common sense view
[A] Context
The description given to the motion of any object depends upon the perspective of the observer.
- A reference frame is the name given to the coordinate system to which an observer (or group of observers) refers measurements.
- Relativity is concerned with the relationship between measurements referred to different reference frames.
[B] Results: Galilean transformations
Key Point 1.9
The relationships between the positions, velocities and accelerations of a particle, P, assigned in two reference frames, A and B, in uniform relative motion are![]() ![]() ![]() They are based on the assumption that time is simple. |

Analysis
First consider 1D case:
- Alison stands by road (frame A)
- Billy passes along in car (frame B)
- Plane passes overhead
- Then xPA=xPB+xBA
- Here xPA is position of P w.r.t. A (1D vector from A to P)
- Differentiating w.r.t. time:
vPA=vPB+vBA
- Here vPA is velocity of P w.r.t. A
Now consider general (2D) case:
Inspection of figure gives first equation
locates P w.r.t origin of A
locates origin of B w.r.t origin of A
- note order of subscripts
Differentiating w.r.t time gives
and thence the second equation:
is velocity of P w.r.t A
is velocity B w.r.t A
Differentiating w.r.t time once more gives
and since
is constant:
[C] Status of results
These results are- consistent with common sense
- practically correct for ‘slow’ kinematics
- wrong for ‘fast’ kinematics, where ‘fast’ signifies involvement of speeds comparable with speed of light, c.
Learning Resources
![]() | HRW Chapter 4.8-9 |
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