> For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.
but this seems to support what I say - there is no collision occurring in a vacuum. What is the expelled air colliding with?
You can also see this by using newton's third law (equal and opposite reactions). The air is accelerating and the only other thing for it to act on is the balloon in equal and opposite fashion.
And just as an aside, IIRC conservation of momentum only applies to your standard physics objects, real objects make noises and sometimes permanently deform. This isn't usually a significant source of error but its neat to think about how if you were playing pool on a frictionless physics surface the difference between the models predictions of where the balls go and where they actually go (very very small difference) could be directly and perhaps entirely attributed to the noise they made on collision.
You might be confusing conservation of momentum and energy with respect in the context of elastic and inelastic collisions.
In a perfectly elastic collision, both momentum and kinetic energy are conserved.
As you say, many real collisions are inelastic to a significant degree. In these cases, momentum is still conserved, but the kinetic energy is converted to another form of energy.
Conservation of linear and angular momentum are fundamental and exact laws of nature resulting from translational and rotational invariance.
No, I don't think so. If you try to apply conservation of momentum as absolutely as conservation of energy (and that linked physics page states it in simple absolute terms) you can quickly encounter gaps because real objects tend to have less than their theoretically conserved momentum due to permanent deformations and interactions with the environment, or the situation involves friction in any way.
Conservation of energy always holds, whereas conservation of momentum has several important caveats and exceptions. Seemed worth pointing that out with an anecdote that amused me.
Hmmmm, actually can you explain a little more about 'momentum is still conserved'? In the cases that I'm pointing out momentum as a measurable property seems clearly not conserved, whereas the energy is (just transformed).
Same way a rocket does. That is, don't treat it as if there's a need for a second object.
The release of air is applying a force in whatever the balloon still has in the direction of travel, even though it's going on the other direction.
Imagine your sitting on a office chair with wheels. If you're holding a large weight and suddenly throw it forward, the chair will roll backwards. This would happen in a vacuum too.
This is a nice way to express it, imo. I also think it's possible to interpret what happens differently. A balloon or something in space doesn't have anything to move against, whereas the chair's wheels are on the floor. When you move the weight in an environment without anything to respond to, ie in suspension in a vacuum, there is no opposite to respond or work against. Both seem possible to me - that a chair+person-with-weight is capable of generating it's own momentum and that nothing happens in space, in a vacuum.
