Disc brakes work differently than traditional systems you find on some multi-speed bicycles. They have a rotor, or metal disc, that turns with the wheel. Brake pads press against the rotor, as opposed to the rim of the wheel. A disc brake system on a mountain bike would be similar to one on any style of bicycle. However, they often are found on mountain bikes. When a disc brake squeaks, that generally means the rotor is dirty.
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Pour a small amount of rubbing alcohol on a clean towel.
Flip the bike over so it rests on the handlebars and seat. This will give you access to the rotor. Look for a metal disc sitting in the middle of one wheel, probably the rear one.
Fold the towel over the rotor at the center of the alcohol spot. The goal is to have one-half of the wet area resting on the inside of the rotor and one-half on the outside.
Turn the wheel with your free hand. As the wheel rotates, so will the rotor. Keep the towel in place for approximately 30 seconds.
Wet the towel again with the rubbing alcohol on a clean area. The first spot will have dirt and grease on it. Repeat the process several times, re-wetting the towel each time .