[geocentrism] Re: Angular momentum
- From: Mike <mboyd@xxxxxxxxxxxx>
- To: geocentrism@xxxxxxxxxxxxx
- Date: Sat, 23 Oct 2004 15:55:12 +0100
Mike wrote:
> On www.midclyth.supanet.com read the article entitled,
> "The laws of physics." (Appears under "The universe"
> heading on the home page.) It was written today,
> following our discussions on this forum.
I think I see what's wrong with your maths.
Inequality (1) was derived from the difference in kinetic energy before
and after the collision. In the formula for KE where the velocity is
squared, the dot product (or scalar product) is used so the inequality
you derived is between scalars, not vectors. The roots of these scalars
(u1, v1, u2 and v2) are therefore scalar quantities as well and actually
represent the particles before and after *speeds*.
Equality (2) was derived from the particles' momentum equations and the
quantaties u1, v1, u2 and v2 represent the particles before and after
*velocities*.
You cannot therefore equate the scalar quantities u1, v1, u2 and v2 in
(1) with the vector quantities by the same name in (2).
It seems to me that you are confusing speed with velocity. Assuming
their masses are the same, the *speed* of each particle may be less
after the collision but their combined *velocity* will be the same. The
amount by which one particle's speed is reduced is balanced by the
amount by which the other particle's speed is reduced when the
directions of the speeds (velocities) are taken into account.
Regards,
Mike.
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