scalar momentum and vector energy

[freefall]

If we expressed a system's momentum as a scalar (e.g. added up all of the |mg|'s), would that quantity be conserved?

 

What if we turned energy into a vector that points in the direction of a system's momentum [e.g. (1/2)mv^2 * (mv/|mv|) ] ? Would that vector be conserved, as momentum is?

 

Just curious, because it seems that we could easily have defined an "energy vector" or a "momentum scalar."

[JustStuit]

Energy is only a scalar. You cannot put a direction on energy, the energy may cause the object to move in a direction but it is still a scalar.

Momentum would not be conserved as a scalar because you rely on the negative momentums in order to put change in momentum as zero most of the time. A collide and stick problem all in one direction may still conserve momentum, but what use is momentum as a scalar anyway?

[swansont]

All conserved quantities stem from a symmetry in nature. With momentum it is a translation, which implies a vector. With energy, it is time, which is not a vector.

[s pepperchin]

since momentum is a vector and is conserved in a system, that would mean that the scalar or absolute value of the momentum as you put it would also be conserved since that is simply the magnitude of the momentum. This however does not mean that all systems with the same magnitude of the momentum are the same.

[5614]

A good example is if you start with an initial momentum of 0 and then shoot two objects (same mass) off in opposite directions (same velocity) then the Conservation of Momentum is still kept as the momentum of each of the two bodies cancel each other out.

 

If you took the magnitudes of each momentum then it would be a non-zero value and so momentum would not have conserved, therefore you cannot do that (take the magnitude of the momentum).

[s pepperchin]

A good example is if you start with an initial momentum of 0 and then shoot two objects (same mass) off in opposite directions (same velocity) then the Conservation of Momentum is still kept as the momentum of each of the two bodies cancel each other out.

 

If you took the magnitudes of each momentum then it would be a non-zero value and so momentum would not have conserved' date=' therefore you cannot do that (take the magnitude of the momentum).[/quote']

 

that is why no one cares about the magnitude of the momentum vector.

 

and going back to the comment about energy as a vector it is not a vector. When you define energy you define the energy at a point in space at a moment in time. If it is changing then you can calculate the energy flux and that would be a vector.