1. “Galilean” Relativity
© D Hoult 2011

7. The velocities stated above are, of course, velocities

8. The velocities stated above are, of course, velocities relative to third body, the ground

9. The velocities stated above are, of course, velocities relative to third body, the ground
In one second, A moves 3 m to the right and G moves 2 m to the left

10. The velocities stated above are, of course, velocities relative to third body, the ground
In one second, A moves 3 m to the right and G moves 2 m to the left
To find the velocity of G relative to A, imagine yourself to be A

11. The velocities stated above are, of course, velocities relative to third body, the ground
In one second, A moves 3 m to the right and G moves 2 m to the left
To find the velocity of G relative to A, imagine yourself to be A
A will see G moving at 5 ms-1 in the

12. The velocities stated above are, of course, velocities relative to third body, the ground
In one second, A moves 3 m to the right and G moves 2 m to the left
To find the velocity of G relative to A, imagine yourself to be A
A will see G moving at 5 ms-1 in the negative sense

13. The velocities stated above are, of course, velocities relative to third body, the ground
In one second, A moves 3 m to the right and G moves 2 m to the left
To find the velocity of G relative to A, imagine yourself to be A
Similarly, G will see A moving at 5 ms-1 in the positive sense

14. To find the velocity of G relative to A we simply subtract the velocity of G (relative to the ground) from the velocity of A (relative to the ground)

15. To find the velocity of G relative to A we simply subtract the velocity of G (relative to the ground) from the velocity of A (relative to the ground)
VG relative to A = VG – VA

16. To find the velocity of G relative to A we simply subtract the velocity of G (relative to the ground) from the velocity of A (relative to the ground)
VG relative to A = VG – VA
VG relative to A = – 2 – 3 = – 5

20. We know the relative speed of A and G (magnitude 5 ms-1)

21. We know the relative speed of A and G (magnitude 5 ms-1) and that A has measured the speed of p to be of magnitude 10 ms-1 relative to himself

22. We know the relative speed of A and G (magnitude 5 ms-1) and that A has measured the speed of p to be of magnitude 10 ms-1 relative to himself
We might want to transform the measurement made by A to find the speed of p relative to G

23. Imagine that p was stationary relative to A

24. Imagine that p was stationary relative to A
Clearly, in this case, the speed of p relative to G is the same as the speed of p relative to A

25. In this case to find the speed of p relative to G, we must

26. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G

27. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G
Vp relative to G =

28. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G
Vp relative to G = 5

29. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G
Vp relative to G = 5 +

30. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G
Vp relative to G = 5 + (–10) =

31. In this case to find the speed of p relative to G, we must add the speed of p relative to A to the speed of A relative to G
Vp relative to G = 5 + (–10) = – 5 ms-1

32. Frames of Reference

33. Frames of Reference
A frame of reference is simply

34. Frames of Reference
A frame of reference is simply a set of axes and

35. Frames of Reference
A frame of reference is simply a set of axes and a clock

36. Consider two observers, A

37. Consider two observers and B

38. at t = zero, A and B are very close together

40. point p is observed by A and B

41. In A’s frame of reference p has coordinates
x, y, z

42. In B’s frame of reference p has coordinates
x’, y’, z’

43. at t = 0

44. at t = 0
x’0 = x0 y’0 = y0 z’0 = z0

45. A and B have a relative velocity of magnitude u directed parallel to their x axes

46. Some time later we have

49. The distance A B is equal to

52. Now A and B attribute different values to the x coordinate of point p

53. It is clear that x’ =

54. It is clear that x’ = x – ut

55. Between time zero and time t the change in position of p relative to A is

56. Between time zero and time t the change in position of p relative to A is

57. Between time zero and time t the change in position of p relative to A is x – x0

58. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is

59. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is

60. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0

61. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0
we saw that x’0 = x0

62. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0
we saw that x’0 = x0
and x’ = x – ut

63. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0
we saw that x’0 = x0
and x’ = x – ut
(x’ – x’0) = (x – x0) – ut

64. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0
we saw that x’0 = x0
and x’ = x – ut
(x’ – x’0) = (x – x0) – ut
dividing by t gives

65. Between time zero and time t the change in position of p relative to A is x – x0
Between time zero and time t the change in position of p relative to B is x’ – x’0
we saw that x’0 = x0
and x’ = x – ut
(x’ – x’0) = (x – x0) – ut
dividing by t gives
v’ = v – u

66. v’ = v – u

67. v’ = v – u
v is the velocity of p relative to A

68. v’ = v – u
v is the velocity of p relative to A
u is the velocity of B relative to A

69. v’ = v – u
v is the velocity of p relative to A
u is the velocity of B relative to A
v’ is the velocity of p relative to B

70. v’ = v – u
v is the velocity of p relative to A
u is the velocity of B relative to A
v’ is the velocity of p relative to B
this equation confirms the relation we used instinctively when combining relative velocities

71. v’ = v – u
v is the velocity of p relative to A
u is the velocity of B relative to A
v’ is the velocity of p relative to B
this equation confirms the relation we used instinctively when combining relative velocities
and…

72. v’ = v – u
v is the velocity of p relative to A
u is the velocity of B relative to A
v’ is the velocity of p relative to B
this equation confirms the relation we used instinctively when combining relative velocities
and… is wrong !