Finding Maximum θ for Apparatus Not to Roll Right

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SUMMARY

The discussion centers on determining the maximum angle θ at which a solid cylinder apparatus, consisting of a central cylinder and two disks, can be pulled without rolling to the right. The key equation involved is τ = Fr sinθ, which relates torque to force and angle. Participants highlight the importance of considering both the torque from the thread and the friction force, indicating that the frictional torque plays a critical role in stabilizing the apparatus. The consensus is that the maximum θ is influenced by the balance of these torques.

PREREQUISITES
  • Understanding of torque and its calculation using τ = Fr sinθ
  • Knowledge of angular and translational kinematics
  • Familiarity with the concepts of friction and its effects on rolling motion
  • Basic principles of mechanics related to solid bodies in motion
NEXT STEPS
  • Study the effects of friction on rolling motion in detail
  • Explore advanced torque calculations in rotational dynamics
  • Investigate the relationship between angular acceleration and torque
  • Learn about the stability of rolling objects under various forces
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in mechanics, particularly those studying rotational dynamics and the effects of forces on motion.

usamo42j
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Homework Statement


The apparatus in the diagram consists of a solid cylinder of radius 1 cm attached at the center to two disks of radius 2 cm. It is placed on a surface where it can roll, but will not slip. A thread is wound around the central cylinder. When the thread is pulled at the angle θ = 90◦ to the horizontal (directly up), the apparatus rolls to the right. Which below is the largest value of θ for which it will not roll to the right when pulling on the thread?

The figure can be found at www.aapt.org/physicsteam/2012/upload/WebAssign-exam1-2011-1-4.pdf (Problem 13)

Homework Equations


τ=Fr sinθ
I'm not sure about others; maybe the ones relating angular/translational kinematics


The Attempt at a Solution



I'm confused. Isn't the only torque caused by the force on the thread, so wouldn't the discs always roll to the right?...
 
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hi usamo42! :smile:
usamo42j said:
Isn't the only torque caused by the force on the thread, so wouldn't the discs always roll to the right?...

what about the torque of the friction force? :wink:
 

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