Re: [Phys-l] Equations (causal relationship)

[Brian McInnes <bmcinnes@pnc.com.au>]

On 01/05/2006, at 3:00 PM, John Denker wrote:


> Surely you know that displacement vectors add.
>    -- 1 meter north plus 1 meter west equals 1.414 meters northwest

Such displacement vectors do not occur at the same time - the notion  
is that the displacement to the north is followed by a displacement  
to the west and the final position of the particle is away to the  
north-west.
> Surely you know that velocity vectors add
>    -- wind triangle:  aircraft velocity (relative to air)
>       plus wind velocity (relative to ground)
>       equals aircraft velocity (relative to ground)
>       [with due regard to sign conventions]

Yes, I do.  In your example the aircraft has has a motion which is  
described and measured as its velocity and the value of that velocity  
will depend on what frame of reference one wishes to measure it in -  
with respect to the air, with respect to the ground or, if one  
wishes, with respect to the passengers in the plane.  In each frame  
there is only one value for the velocity
>  From there it should not be much of a stretch to understand how
> acceleration vectors add.

No, since your analogies with displacement and velocity do not  
correspond to your claim - that a particle can have more than one  
acceleration at once - it seems to be a not only a stretch but an  
unbridgeable chasm.
> > If what is written is a claim that when a particle has three forces
> > acting on it there is a separate acceleration associated with each
> > force, well, I just can't buy that.
>
> It just amazes me how people can form such strong opinions without
> a shred of objective experimental and/or theoretical support.
>
> Acceleration is a vector.  Force is a vector.
> The math is the same, and the physical interpretation is the same.

Again, I must write that I cannot agree.  Forces are external to a  
particle, there can be many (or none) of them acting,  Acceleration  
is an attribute of a particle - as such, in a given reference frame,  
it must have a single value.

Brian McInnes