If you look at the saw, you can see it’s made of lots of little triangle teeth. When you “cut” the metal, you are rubbing the little teeth over it to break off little pieces and wear bits away. That means you are using friction in cutting. Friction makes heat (see physics note) and you rub the saw over lots and lots of times, making lots of heat, which gradually spreads out through the metal and makes the bit near your hand feel hotter.
physics note: Friction makes materials hot because rubbing one surface over another stretches the bonds between atoms in the surfaces. When the surfaces aren’t in touch any more, the atoms spring back, releasing energy as heat.
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