Relative Motion with Two Moving Figures: What's the Best Way?

[mewmew]

What is the best way to think about relative motion with two moving figures? Perhaps it depends on the problem but in general is it best to just imagine one of the figures as stopped and the other moving with its relative velocity, or could you run into some problems that way? Thanks for any information.

 

[spacetime]

Well, mewmew, there are laws that will tell you which methods can be applied and which cannot.

1. Newton says motion has meaning with respect to a frame and independent velocity has no meaning. So, if it is just about velocities ( no accelerations, which, Newton says, are not just relative ) you may well assume one to be at rest and the other moving.

2. But again Newton says that inertial frames are required to apply his equations. So, if you are trying to use F=ma or "every action has equal and opposite reaction" be sure you are in an inertial farme, that is, you can't just imagine an accelerating particle to be at rest otherwise you might find accelerations without forces and bodies just starting off without any forces acting on them.

3. Special relativity also "prefers" inertial frames.

4. General relativity doesn't.

5. Maxwell's equations - well I am not sure.

So, basically it depends upon the laws you want to apply. if the law requires an inertial frame, be sure to give it that.

spacetime
www.geocities.com/physics_all/index.html

 

[Gonzolo]

The first inportant thing is whether the relative speed comparable to light speed or not. This tells you whether to use Special Relativity or Newtonian Mechanics.

Then you are usually better of to quote: "imagine one of the figures as stopped and the other moving". It is what is always done in school no? In most problems, the surface of the Earth is stopped, and something is moving relative to it.

 

[dav2008]

What is the best way to think about relative motion with two moving figures? Perhaps it depends on the problem but in general is it best to just imagine one of the figures as stopped and the other moving with its relative velocity, or could you run into some problems that way? Thanks for any information.

If you are talking about non-relative motion then the way I learned it is just by using vectors and a subscript notation.

Let's have g denote the ground, a denote object a and b denote object b.

Now, let's say you are given that a is moving at 3 m/s North and b is moving 2 m/s South (I'm using simple directions to make it..well more simple but you can use this for any direction theyre going)

You have(The subscript just means velocity of a with respect to g(ground)) V_a/g = 3 j
V_b/g = -2 j

Now if you are looking for the velocity of a with respect to b (V_a/b) you treat the subscripts as fractions and the addition as multiplication


V_a/b=V_a/g + V_g/b

Now you know that V_g/b is just - V_b/g

So you have

V_a/b=V_a/g + -V_b/g

V_a/b=3 j -(-2 j) = 5j

I hope that's what you are asking about, and someone feel free to correct me if I made a typo or something.

This probably seems confusing for such a simple thing, but it helps me out in these types of problems