Shaking/Vibrating Steering Wheel
 

Does anybody know why my (2011 mazda 3) steering wheel would be shaking uncontrollably when I brake? (Sometimes) Or start vibrating/minimal shaking when I'm driving (also only sometimes) I feel like it could be my brake pads might be worn... but I am unsure, because I don't see how brake pads would affect the driving part.

A little bit could be caused by worn brake pads. “shaking uncontrollably” more likely due to warped or cracked rotor, or worse a bad/broken wheel bearing or spindle. The latter two are significantly more dangerous. Pull the wheel and take a look. Broken suspension/steering parts can also cause this; also not a good situation.

Thanks I will definitely have a look!

Brakes and suspension are serious stuff, If you aren't fully clued up I would strongly suggest taking it to a professional. Your life depends on your car's safety.