Calculating Relative Motion of A, B, & C: Agree?

In summary, the conversation discusses the concept of calculating the speed of objects in different frames of reference and whether these calculations will always agree reciprocally. It is confirmed that the answer is "yes" and this can be achieved through methods such as reciprocal (Doppler) radar measurements and the relativistic addition of velocities equation. The post from Jorrie clarifies that the addition of velocities equation is all that is needed to theoretically perform the calculation.
  • #1
wsellers
13
0
This is indirectly addressed in some posts but I can't find a direct answer to the following: consider moving frames A, B, and C (e.g., A, B, and C are 3 trains moving at different speeds on the same track; or A is a train, B is a person walking inside the train holding a tray, and C is a wind-up toy moving along the tray; etc.). Now observers in each frame calculate the speed of the objects in the two other frames relative to them. Will these calculations always agree reciprocally--e.g., will a person in A calculate a speed for the motion of C that is the same (magnitude) as the speed calculated by a person in C for the motion of A? I believe the answer is "yes" but would like confirmation.
 
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  • #2
Yes. The speed of C with respect to A (as measured by A) is the same as the speed of A with respect to C (as measured by C).
 
  • #3
What Doc Al mentioned can be accomplished by e.g. reciprocal (Doppler) radar measurements. Wsellers mentioned calculated speeds, for which the relativistic addition of velocities equation can be used to verify the answer in both directions, first with positive velocities and then with negative velocities.
 
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  • #4
Thanks to both for your prompt replies! (I wasn't sure that all that was needed to do the calculation theoretically was the addition of velocities equation, so the post from Jorrie clarifies that.)
 

1. What is relative motion?

Relative motion is the movement of an object in relation to another object. It takes into account the motion of both objects and their positions relative to each other.

2. How do you calculate relative motion?

To calculate relative motion, you need to determine the velocity of each object and the distance between them. Then, you can use the formula Velocity (of A relative to B) = Velocity (of A) - Velocity (of B) to calculate the relative motion of object A with respect to object B.

3. What is the difference between relative motion and absolute motion?

Relative motion takes into account the motion of one object with respect to another, while absolute motion refers to the motion of an object with respect to a fixed point in space.

4. Can relative motion be negative?

Yes, relative motion can be negative. This means that the two objects are moving in opposite directions or that one object is moving faster than the other.

5. How does the motion of object C affect the relative motion of objects A and B?

The motion of object C can affect the relative motion of objects A and B if it is moving in the same direction or opposite direction as either of the objects. This will change the overall velocity and relative motion of the system.

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