A tear is a type of scratch used by turntablists. It is made from moving the record on the turntable

Phonograph

The phonograph record player, or gramophone is a device introduced in 1877 that has had continued common use for reproducing sound recordings, although when first developed, the phonograph was used to both record and reproduce sounds...

 by hand.

Technique

The tear is much like a baby scratch in that one does not need the fader to perform it, but unlike a baby scratch, when the DJ pulls the record back he or she pauses his or her hand for a split second in the middle of the stroke. The result is one forward sound and two distinct backward sounds. This scratch can also be performed by doing the opposite and placing the pause on the forward stroke instead. A basic tear is usually performed with the crossfader open the entire time, but it can also be combined with other scratches such as flares

Flare (scratch)

Flare is a type of scratch used by turntablists. It is made from a combination of moving the record on the turntable by hand and quick movement of the crossfader.The flare was invented by its namesake, DJ Flare, in 1991, but was further developed by DJ Q-Bert....

for example by doing tears with the record hand and cutting the sound in and out with the fader hand.