An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle is supported. In the latter case, a bearing or bushing sits inside a central hole in the wheel to allow the wheel or gear to rotate around the axle. Sometimes, especially on bicycles, the latter type axle is referred to as a spindle.
How would I find the acceleration of the above spindles (both left and right instances)? The spindles are composed of two disks with a cylindrical solid axle. The left spindle is unwinding the string as it rolls and the right spindle is winding the string as it rolls. Static friction is present...