Re: Conservation of angular momentum

On 2007-05-28, Peter <Poakfield@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 linear momentum, but rotating
around the whole system's centre of mass with an angular momentum equal
to the negation of the angular momentum in 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 and angular momenta 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 of momentum to 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, and angular momentum is
conserved. Spaceship and lever orbit each other a bit like a pair of
binary stars.
.

Relevant Pages

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