The "rules of vectors and trig" apply to vectors. It does not matter whether they are "displacement", velocity, acceleration, or force vectors.
Ok so I have a very basic clarification question about vector mechanics.
It is obvious that with displacement vectors the rules of vectors and trig apply to combining them. I cannot, however, see why we should assume that force vectors, velocity vectors etc should combine in the same way. Of course I know that they do but is this something that can be proved on paper or is it just shown experimentally?
I hope I have explained myself properly and I will try to rephrase my question and provide an example if I am not being clear.
Thanks for your help!
The "rules of vectors and trig" apply to vectors. It does not matter whether they are "displacement", velocity, acceleration, or force vectors.
Yeah I see that and appreciate that it is the case, but my question is how do we know that velocity, acceleration and force should combine in the same way?
Ok lol
What I mean then is how do we know that they are vectors? Sure they have magnitude and direction, but why should they combine according to geometrical methods?
(By the way I'm not doubting that they do! I'm just trying to understand more fully.)
thanks
Because vectors have a geometric representation (i.e. the arrows in space, ergo showing the length/magnitude and direction). This means they have to follow the properties of geometry.
I think you are over-thinking things. It is a question of DEFINITION. A vector is defined to be a quantity that has magnitude and direction. Therefore, IF a quantity has magnitude and direction, it is a vector. Geometric objects have to follow rules of geometry. Since a vector HAS a geometric representation, it must follow the rules of geometry.