Re: Angular momentum

Ditto wrote:
Fallingeagle wrote:
Can someone explain Why the total angular momentum of a system with a
pully, and two masses joined by a massless string overt the pully
equals the angular momentum of the pully + the angular momentum of the
two masses?

why: L(sys) = L(pully) + L(masses)

I omega + m1 * v * r + m2 * v * r

This is what I do not understand:

the spin (AM) of the pully is caused by the the two masses, why is the
total spin not just the spin of the pully?

also: what is spin (angular momentum)....really??

For a point particle, angular momentum is defined as the cross product
of it's radial position vector r and it's linear momentum. i.e L = r x
p.

For a system of particles, total angular momentum = sum(k = 1 to n)
[L_k]
So for your pully system, Ls = Lp + Lm1 + Lm2

Thing to note is that angular momentum of a system depends on choice of
origin of coordinate system, and that a particle moving in a straight
line has a non-zero angular momentum.

If you are right then my explanation must be wrong.

OK. Let's suppose that the system starts out without any velocity in
any part of the system and that the first mass is more massive than the
second. So the first mass starts to move downward due to
gravity(assuming that is part of the probelm) As the masses accelerate
the pulley is accellerating. Therefore if angular momentum is conserved
and the pulley is exhibiting angular momentum then the masses must be
as well.

Until one of these weights collides with the pulley no rotational
components will be present, unless you have them swinging about like
pendulums. I think this problem neglects these effects. Am I wrong in
thinking that no angular velocity means zero angular momentum?
From
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
I see
L = mvr sin θ
and the definition
L = r x p
The 2D version should be adequate for this problem. Here already we see
a theoretical conflict in the definition. The cross product exists for
a 3D system only. Therefore no general dimension solution exists under
this definition.
If the mass travels a straight line then a pure radial measure would
require r at infinity.
theta would then be zero for any finite velocity. This could be a neat
calculus puzzle but since the center of motion is not strictly
specified this may be a broken study of the system. Angular momentum is
merely a shortcut method of handling the component momenta of a rigid
object's constituent particles and their corresponding accelerations. A
rotating object is an accelerated system.

This complexity is at the edge of my understanding and I look forward
to learning something here. I am entirely open to being wrong. Please
find where I have gone astray.

-Tim


Hope this helps.

.

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