Can momentum be hidden to human eyes like how kinetic energy can be hidden as heat?
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Yes and no.For instance, in an electromagnetic system, momentum can be transferred to the electromagnetic field, which is invisible to human eyes at most frequencies. Therefore, momentum can be "hidden" in the electromagnetic field.
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Heat is carried by the random momenta of the particles in matter.
Momentum is a vector and conservation has to do with the direction too. If you heat matter with a laser in a given direction, the momentum of the beam will also be transferred to the mass , but the velocity (mv) will not be measurable , due to the large mass that absorbs the impact. In this sense one will get a collective momentum vector for the mass undergoing heating by laser.
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