Solving Confusions on Pulling a Spool

Thread starter member 731016
Start date Feb 21, 2023

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SUMMARY

This discussion centers on the mechanics of pulling a spool and the implications of static friction and motion. Participants clarify that the Uniformly Accelerated Motion (UAM) equations are not applicable due to the spool's cylindrical shape, which prevents it from being treated as a point particle. Static friction does not perform work as it does not cause displacement at the point of contact, and the net work-energy theorem does not include static friction in its calculations. The conversation also explores the relationship between the distance moved by the spool and the hand, emphasizing that when the spool rolls without slipping, the hand moves a distance equal to the spool's radius plus the distance it rolls.

PREREQUISITES

Understanding of Uniformly Accelerated Motion (UAM) equations
Knowledge of static friction and its role in mechanics
Familiarity with Newton's laws of motion
Basic concepts of rotational dynamics and torque

NEXT STEPS

Study the implications of static friction in rotational motion
Learn about the work-energy theorem and its applications in mechanics
Explore the relationship between linear and angular displacement in rolling objects
Investigate the effects of different shapes on motion dynamics, particularly cylinders versus spheres

USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of rolling objects and the role of static friction in motion.

Feb 25, 2023

member 731016

haruspex said:

Yes,

No, you are free to define positive separately for each force, each displacement, each acceleration. Just be clear about it and do it consistently through the equations.

If all such variables are along the perpendicular axes, it is a good idea to pick one convention for them all. If not, you could decompose each oblique variable into such components or define the conventions individually.

Many prefer to guess which way each will act and define positive accordingly. That's ok as long as you handle each consistently and accept that some may turn out to have negative values.

That said, there may be cases where the equation does change if you guessed wrongly, but I can only think of quite contrived ones.

Thank you for your reply @haruspex! That is very interesting!

Many thanks!