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This applies same for

moment = r x F

Linear velocity of a particle rotating about an axis = omega x r

Let's look at the moment, r and F is perpendicular to each other, but why is the moment perpendicular to both r and F? Shouldn't the rotation be in the direction of a tangential force? I'm confused.. Why is a cross product being treated like a conventional multiplying sign when we are actually finding a vector perpendicular to both of the displacement vectors?