Is tear both a noun and a verb?

Yes, the Word "tear" can be used as both a noun and a verb.

Noun: a hole or a split in a solid material caused by tearing, or a drop of liquid that comes from your eye when you cry.

Verb: to split a solid material by pulling two pieces apart to destroy (holding a piece of paper in two places and pulling to tear it apart or tear a piece off); to rip.