If your steering wheel turns when you hit your brakes, it is most likely due to an issue with your brake rotors. When you press on the brake pedal and the car slows rapidly, it can cause the rotors to warp/bend. This results in a pulsating feeling in your brake pedal, as well as vibrations in the steering wheel. You can also hear a squealing sound when you stop, which could mean that your brake pads are worn out.
The best way to diagnose this is by checking for any noises or sounds coming from the brakes when you slow down. If you hear squealing or feel a pulsating sensation in the brake pedal, you might have warped rotors. It is recommended that you take your car to a mechanic who can examine the rotors and determine if they need replacing.
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