Making a spool slide without rolling

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AI Thread Summary
The discussion focuses on determining the direction in which a spool can be pulled without rolling on a horizontal surface. It is suggested that pulling from the top (direction I) may allow the spool to slide without rotation, as the string would not unravel. Participants express confusion about how the inner and outer radii of the spool affect the torque and motion. The concept of the instantaneous axis of rotation is introduced as a hint to understand the mechanics involved. Ultimately, the key point is that pulling in specific directions can lead to translational movement without causing the spool to roll.
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1. Homework Statement
As shown in the figure to the right, a spool has outer radius R and axle radius r. A string is wrapped around the axle of the spool and can be pulled in any of the directions labeled by I, II, or III. The spool will slide to the right without rolling on the horizontal surface if it is pulled in which direction(s)?

Homework Equations


τ=Fr
F=ma

The Attempt at a Solution


I thought all the forms of pulling would cause rolling, since each pull will exert a torque on the spool, but that's not right. I'm not sure if it's different because there's an inner and outer spool though, and if so, how to factor that into the problem.
 

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i think it would be 1, since if you are pulling it from the top, the string won't unravel (normally) and the spool won't have rotation just translation
 
Hint: If the spool rolls without slipping, what would be its instantaneous axis of rotation?
 

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