Making a spool slide without rolling

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SUMMARY

The discussion centers on determining the direction(s) in which a spool will slide without rolling when pulled by a string wrapped around its axle. The key conclusion is that pulling the string from the top (direction I) allows the spool to slide without rolling, as it does not create a torque sufficient to induce rotation. The concepts of torque (τ=Fr) and force (F=ma) are essential in analyzing the forces acting on the spool. Understanding the relationship between the inner and outer radii of the spool is crucial for solving the problem accurately.

PREREQUISITES
  • Understanding of torque (τ=Fr)
  • Familiarity with Newton's second law (F=ma)
  • Knowledge of rotational motion concepts
  • Basic principles of friction and slipping
NEXT STEPS
  • Study the concept of instantaneous axis of rotation in rigid body dynamics
  • Learn about the conditions for rolling without slipping
  • Explore the effects of different pulling angles on torque generation
  • Investigate the mechanics of spools and pulleys in physics problems
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Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for practical examples to illustrate these concepts.

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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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