Things to check...

Loosen the belt off the tentioner, lower passenger side, where your alternator is located, check the the grooved pulley to see if the bearing is seized, or has any movement which would cause in to turn nonconcentric.

Also, a bad alternator can affect your battery, have a local auto store check the voltage, should be 12-13 volts. If the alternator is defective, signs of electrical problems will occur. Do your headlights dim under acceleration?