Re: Conservation of angular momentum

On May 29, 7:37 am, Ben C <spams...@xxxxxxxxx> wrote:
On 2007-05-29, Peter <Poakfi...@xxxxxxx> wrote:





On May 28, 5:45 pm, Ben C <spams...@xxxxxxxxx> wrote:
On 2007-05-28, Peter <Poakfi...@xxxxxxx> wrote:

On May 28, 11:29 am, "Greg Neill" <gneill...@xxxxxxxxxxxxxxx> wrote:
[...]
To simplify things (or complicate them) let us assume this test is
carried out in a spaceship at rest in space. The equal-arm lever is
mounted on a vertical axis anchored on a table secured to the floor of
the spaceship. Do you think you can accelerate the spaceship pushing
on the middle of the right arm of the lever?

Not by pushing, but you can't push the spaceship along by leaning
against the wall from the inside either.

You can move the spaceship hull back and forth by firing a BB gun at the
lever. But not by pushing. There will be a force through the spindle
attaching the lever to the table that's transferred to the floor of the
spaceship through the table's feet. But there will be an opposing force
also transferred to the floor through the feet of the astronaut who's
pushing the lever. So no net force on the spaceship hull.

But suppose you fire a ball-bearing at the lever. As the BB leaves the
gun, the gun, and therefore the spaceship (connected to the gun through
the astronaut and his boots) accelerate in the opposite direction to the
ball-bearing. Note also that if the gun is fired in a direction that
doesn't intersect the hull's centre of mass, that the hull will also
start to rotate. Once the ball-bearing hits the lever, the spaceship
decelerates again leaving it with no linearmomentum, but rotating
around the whole system's centre of mass with anangularmomentumequal
to the negation of theangularmomentumin the rotating lever[1].
Overall the spaceship hull will have a small change of position, since
now the BB is on the other side of the room, but the centre of mass of
spaceship + BB + astronaut + everything is in the same place as it
always was, and the total linear andangularmomenta of the system have
remained constant at all times.

I think it's quite helpful to think about the force on the nail
attaching the lever to the table. If the nail wasn't there, the lever
would accelerate away as well as rotating. Since it doesn't, there must
have been a transfer ofmomentumto the nail, and therefore also to
whatever the nail's attached to.

[1] Interesting also to think about the situation in which nail is not
through the centre of mass of the lever, but instead through one end.
Once the lever has been set spinning, there will be a force of constant
magnitude but continuously changing direction on the nail. What happens
to the spaceship hull? It gyrates in the opposite direction, kept in a
sort of orbit around the lever by the force on the nail. The centre of
mass of the whole system never changes, andangularmomentumis
conserved. Spaceship and lever orbit each other a bit like a pair of
binary stars.

I think you are right. I have never questionedconservationof linear/
angularmomentum. But there are many examples where linearmomentum
converts intoangularmomentumand vice versa. Think of a car, what
kind ofmomentumstarts moving it? Is it linear? The car has linear
momentum. Do the wheels haveangularmomentum? What happens in the
engine? Where these momenta come from?

It's all the samemomentum.Angularmomentumis just another way of
looking at the situation. You pick an origin, measure everything's
radius to that origin, and work in a world in which everything is "x r".
This is a powerful way of doing things and saves you integrating point
masses' positions in rigid bodies all the time.

No new physics I don't think, just new maths. But the fact thatangularmomentumis conserved (which is a stronger claim than just thatmomentum
is conserved) probably does have something to do with some property of
3D space.- Hide quoted text -

- Show quoted text -

I think the "x r" is not necessary. The fundamental entity is momentum
m|v|, which in the absence of a net external force in the direction of
motion of whatever, is conserved. I do think that this is due to some
characteristic of 3D space.

Peter

.

Relevant Pages

  • Re: Conservation of angular momentum
    ... carried out in a spaceship at rest in space. ... The equal-arm lever is ... I think it's quite helpful to think about the force on the nail ... But there are many examples where linear momentum ...
    (sci.physics)
  • Re: Conservation of angular momentum
    ... carried out in a spaceship at rest in space. ... The equal-arm lever is ... I think it's quite helpful to think about the force on the nail ... But there are many examples where linear momentum ...
    (sci.physics)
  • Re: Conservation of angular momentum
    ... carried out in a spaceship at rest in space. ... The equal-arm lever is ... to the negation of the angular momentum in the rotating lever. ... I think it's quite helpful to think about the force on the nail ...
    (sci.physics)
  • Re: Conservation of angular momentum
    ... spindle attached to something then obviously the linear k.e. ... spaceship some linearmomentumfrom actions inside the spaceship. ... Here's my view of what happens: you shoot the ball out, ... spinning about its COM in the opposite direction to the lever, ...
    (sci.physics)
  • Re: Conservation of angular momentum
    ... spindle attached to something then obviously the linear k.e. ... spaceship) one realizes clearly that it is impossible to give the ... Here's my view of what happens: you shoot the ball out, ... spinning about its COM in the opposite direction to the lever, ...
    (sci.physics)
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