[geocentrism] Re: Angular momentum
- From: Mike <mboyd@xxxxxxxxxxxx>
- To: geocentrism@xxxxxxxxxxxxx
- Date: Wed, 27 Oct 2004 15:06:28 +0100
Dear Neville,
> Furthermore, the physics argument is perfectly straightforward. If
> some kinetic energy is lost in an inelastic collision, then either
> some mass or some velocity, or both, has been lost. But if it's been
> lost, then some linear momentum (which is itself a product of nothing
> more than mass and velocity) has also been lost. It doesn't just pop
> back in again, so as to save a so-called "law."
Kinetic Energy is scalar. The total kinetic energy is just the amount
by which everything is moving. Two objects thrown in the same direction
have the same KE as they would if they were thrown in two different
directions.
Velocity and momentum are vectors. When totalling, momentum in one
direction offsets momentum in another direction. Two objects thrown in
the same direction have more momentum than if they were thrown in two
different directions.
The simplist demonstration of this is two particles of 1kg mass moving
at the same speed in oppoiste directions that collide inelastically. If
they move on the same axis but in opposite directions then the velocity
vectors reduce to *signed* speeds, +ve one way and -ve the other. The
kenetic energy is stil absolute because when we square a -ve we still
get a +ve.
Suppose:
u1 -> 5m/s u2 <- 5m/s
v1 <- 2m/s v1 -> 2m/s
Lets call right positive. Then
u1 = 5
u2 = -5
v1 = -2
v2 = 2
Kinetic Energy:
KEu = 1/2 m u1^2 + 1/2 m u2^2
= 1/2 (5^2 + -5^2)
= 25
KEv = 1/2 m u1^2 + 1/2 m u2^2
= 1/2 (-2^2 + 2^2)
= 16
Momentum:
Pu = mu1 + mu2
= 5 + -5
= 0
Pv = mv1 + mv2
= -2 + 2
= 0
So KEu > KEv but Pu = Pv
i.e. the total kinetic energy reduced but the total momentum stayed the
same.
You may object that I started with 0 momentum so there's none left to
lose. Well that in itself sufficiently demonstrates that KE *can* be
lost without a *necessary* loss in momentum counter to your claim that
"some kinetic energy is lost in an inelastic collision, then either some
mass or some velocity, or both, has been lost."
I have already given you an example of KE reducing while momentum is
conserved where all the velocities are in the same direction. You
rejected it because I relied on the coefficient of restitution to
calculate the velocites. Well, if you are going to claim that momentum
is lost according to conventional physics then you have to use
conventional physics to show it. Likewise if you are going to claim
that conventional physics is inconsistent you have to use assume, for
the sake of argument, that conventional physics is correct and then from
there derive a constradiction - that is what your "laws of physics"
proof attempted, but it contained a *mathematical* error.
Regads,
Mike.
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