When we speak of a reference frame in relativity, it is not necessary for two pe

Question

When we speak of a reference frame in relativity, it is not necessary for two people to share the same "origin" for them to have a common inertial reference frame. Imagine the following situations: Person A is standing on campus near the Physics Research Building (PRB); Person B is riding a bus due east from the football stadium west of the building to the PRB at 20 mph; Person C is riding a bus due west from the PRB to the football Stadium at 30 mph; Person D is standing on a platform waiting for a train in New York; Person E is driving a car east from the PRB, and having stopped at a stop sign is just starting to accelerate, but still has a speed of zero.

1) Is person B in the same reference frame as person A? Why or why not?

2) Is person C in the same reference frame as person B? Why or why not?

3) Is person D in the same reference frame as person A? Why or why not?

4) Is person E in the same reference frame as person A? Why or why not?

5) How many different reference frames are needed to include all of the people mentioned above?

6) What quantity defines a reference frame? (If you are not sure, consider how you determined which of the above people were in the same reference frame; what did they have in common?)

Explanation / Answer

1.

Person B and A are not in same frame. As there is relative velocity of B W.r. t A.

2.

No, person B and C are not in same frame as Frame of B is moving with 60mph relative to C. And vice versa.

3.

Yes, both are stationary w.r.t ground so their relative velocity is zero. They can be considered as same frame with different origin.

4.

No, both are different frame because E has some acceleration so E is a non inertial frame while A is inertial frame w.r. t. Ground or earth.

5.

We need total 4 reference frame as two can be considered in same frame.

6.

Velocity of frame W.r. t to a stationary object or comcan objec and acceleration of frame w.r.t a comman object.

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