If the steering wheel or car shakes when the brakes are applied, it is almost certain that the problem lies with the rotors. This is an important distinction as steering wheel or car vibration can happen for a number of reasons, but if it only happens when the brakes are applied, this isolates the problem. Worn brake pads are another possibility, but if the pads have recently been replaced, then this leaves only the rotors as suspects.
Rotors are the large metal discs that the brakes clamp in order to stop a car. When the brakes are applied, intense heat spreads across the rotors. Normally, the rotor surface is smooth and the heat is dissipated across this area. However, when rotors become worn, pits and grooves appear. When the brakes are applied, the unevenness is transmitted through the brake pedal to the steering wheel and the rest of the car, causing the shaking.
In some cases, rotors are only unevenly worn and can be machined or smoothed out to near their original state. However, if the rotors develop pits or grooves, they are likely to be beyond repair. In that case, it is necessary to purchase new rotors. Brake pads should also be replaced at this time.