Acceleration of a Spindle System with Two Disks and a Solid Axle

AI Thread Summary
To find the acceleration of a spindle system with two disks and a solid axle, consider the dynamics of both spindles: one unwinding and the other winding a string. The presence of static friction ensures that the spindle rolls without slipping, which is crucial for calculating acceleration. The moment of inertia of the disks and the torque generated by the tension in the string must be analyzed to derive the equations of motion. Applying Newton's second law and rotational dynamics will yield the necessary acceleration for both instances. Detailed calculations and specific formulas can be found in the linked response for further clarification.
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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 and the spindle rolls without slipping. Any help would be greatly appreciated.
 
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See my response in the College Level help forum:
https://www.physicsforums.com/showthread.php?s=&postid=168930#post168930
 

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