Sorry if this is Electrical Engineering pre-school. I'm a software guy that hasn't taken a class involving voltages for 10+ years.

I'm working on an Arduino project that will have to be fairly mobile. I'm using a Nema-17 stepper motor that is rated at 12v 1.2a ([link to specs](http://i.ebayimg.com/t/NEMA-17-56-6-oz-1-2A-40N-cm-High-Torque-Bipolar-Stepper-Motor-Reprap-3d-Printer-/00/s/MTUwM1gxNjAw/z/BNMAAMXQhpdRzi~z/%24T2eC16RHJHsFGlMr,jKCBRzi+zQ-4Q~~60_57.JPG)). I'm looking for a suitable battery to power my motor for around an hour. I found a 12v 2000mAh battery ([link to battery](http://rads.stackoverflow.com/amzn/click/B00408X4LU)). This (according to my knowledge) means this battery should be able to power my 1.2a motor for around 1.6 hours. 

My question is; will my motor only draw what it needs(assuming I don't short it) or will the battery pump too much power and fry my motor? Any help Would be great!