Could there be a type of mass that moves in a direction perpendicular to its momentum?

Positive mass moves in the same direction as its momentum and if negative energy exists then it would move in the opposite direction from its momentum.

I was thinking of a type of mass, known as "side mass," that would move in a direction perpendicular to its momentum.

Could this type of mass exist and if so what would determine which direction perpendicular to its momentum it moves in?

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Could there be a type of mass that moves in a direction perpendicular to its momentum?

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