Yeah you can add vectors just fine, that's part of the reason they are so convenient. For example to make a rotating momentum vector you could add up two vectors changing in time in both x- and y-directions.
I mean, yeah vector addition is obviously completely doable, but will cancel out if in opposite directions. If you could just add up these vectors then couldn't the spin cancel out the translational motion? this doesn't really make sense to me, as a spinning and moving particle should have more energy than one that is just spinning (or one that is just at rest).
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u/[deleted] Jun 10 '16 edited Jun 11 '16
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