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Cosmic Adventure 4.9 Relative Motion in Classical Mechanics

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Relative Motion in Classical Mechanics

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Cosmic Adventure 4.9 Relative Motion in Classical Mechanics

  1. 1. Β© ABCC Australia 2015 new-physics.com OBJECTS ON THE MOVE Cosmic Adventure 4.9
  2. 2. Β© ABCC Australia 2015 new-physics.com Relative motion is the motion between two or more bodies. So, in dealing with motion, we have two or more coordinate systems each of which is attached to an observer or an object.
  3. 3. Β© ABCC Australia 2015 new-physics.com Alignment of Systems When the observer and the object are in line as in rectilinear motion, any two coordinate systems can be aligned to each other to form a simpler observation system. 0’ P0’
  4. 4. Β© ABCC Australia 2015 new-physics.com 𝑠 0’ π‘₯β€² P System 1 Primed (β€˜) π‘₯β€²β€² 0’ P System 2 Primed (β€˜β€™) Two Static Reference Systems We start off with two static reference systems, all of which are related to a third object located at P. They are separated by a distance s. To identify them, system 1 will bear a single prime (β€˜) and 2 will bear a double prime (β€˜)
  5. 5. Β© ABCC Australia 2015 new-physics.com 𝑠 π‘₯β€² π‘₯β€²β€² 0’ P When they refer to the same object at P and are collinear, they can be combined into one reference system. But for easier recognition, we prefer to use two in graphics. 0’’ 𝑠 0’ π‘₯β€² P System 1 Primed (β€˜) π‘₯β€²β€² 0’ P System 2 Primed (β€˜β€™) ❢ ❷ Single system
  6. 6. Β© ABCC Australia 2015 new-physics.com Two Reference Systems with Synchronized Timing Now we have set primed two system (O’’) in motion. In the first place we move frame two to coincide with frame one so that they both count their time starting time at t=0. 0’ β†’ 0’’ 𝑠 = 0 0’ π‘₯β€² P 0’’ π‘₯β€² β€² P
  7. 7. Β© ABCC Australia 2015 new-physics.com Time & Period We understand that in telling time we use 𝑑; but in measuring time duration we have to use βˆ†π‘‘. Time is a location in the time scale but duration is a period – a space between two times 𝑑1and 𝑑2. Then: βˆ†π‘‘ = 𝑑2βˆ’ 𝑑1 Time 𝑑 Duration βˆ†π‘‘ 𝑑2 𝑑1
  8. 8. Β© ABCC Australia 2015 new-physics.com 0’ π‘₯β€² P π‘₯β€²β€² 0’’ P 𝑠 = π‘£βˆ†π‘‘ Relative Velocity v If O’’ is on the move away from the starting point at constant velocity v, the relative velocity between them is v. Then after a period of time βˆ†π‘‘ the distance 𝑠 between the two systems will be: 𝑠 = π‘£βˆ†π‘‘
  9. 9. Β© ABCC Australia 2015 new-physics.com π‘₯β€²β€² = π‘₯β€² βˆ’ 𝑣𝑑 π‘₯β€² = π‘₯β€²β€² + 𝑣𝑑 Then the relation between the two systems will be: 0’ π‘₯β€² P π‘₯β€²β€² 0’’ P 𝑠 = π‘£βˆ†π‘‘
  10. 10. Β© ABCC Australia 2015 new-physics.com So these are the two sets of equations employed by classical physics: System x: π‘₯β€² = π‘₯ βˆ’ π‘£βˆ†π‘‘ 𝑦′ = 𝑦 𝑧′ = 𝑧 𝑑′ = 𝑑 System x’: π‘₯ = π‘₯β€² + π‘£βˆ†π‘‘ 𝑦 = 𝑦′ 𝑧 = 𝑧′ 𝑑 = 𝑑′
  11. 11. Β© ABCC Australia 2015 new-physics.com FROM GALILEAN TO EINSTEINIAN Cosmic Adventure 4.10

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