tear (something) on (something)
To cause something to become cut or ripped by snagging or abrading it on something sharp, pointed, serrated, or jagged. I can't believe I tore my favorite dress on a loose nail. He tore the sleeve of his shirt on the exposed sawblade.
tear something on something
to rip something on something sharp or jagged. I tore my pants on the corner of the desk. Mary tore her new skirt on something sharp on the side of the car.