What Happens When a Yo-Yo Rolls Without Slipping?

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SUMMARY

The discussion centers on the mechanics of a yo-yo rolling without slipping, specifically analyzing the forces and torques involved when a force is applied to the string. Participants clarify that when the yo-yo is pulled, it will slide to the right while rolling clockwise if friction is sufficient to prevent slipping. The center of mass (CM) velocity is directed to the right, countering the backward rolling motion caused by the string tension. The final equation derived is F = (3μmg)/(1 + 2b/R), illustrating the relationship between applied force, friction, and motion.

PREREQUISITES
  • Understanding of angular momentum and fixed axis rotation
  • Familiarity with Newton's laws of motion
  • Knowledge of frictional forces and their effects on motion
  • Basic grasp of torque and its calculation
NEXT STEPS
  • Study the principles of rolling motion and friction in detail
  • Learn about torque calculations in rotational dynamics
  • Explore the concept of instantaneous axes of rotation in rolling objects
  • Investigate the effects of varying friction coefficients on motion
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of rolling motion and the interplay of forces in mechanical systems.

  • #31
haruspex said:
I'm not sure what you mean. Direction of linear acceleration or of angular acceleration? CM velocity or CM linear acceleration?
Hi haruspex. I was referring to the linear acceleration and the linear (center of mass) velocity.
 
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  • #32


PhizKid said:
Hi haruspex. I was referring to the linear acceleration and the linear (center of mass) velocity.
Starting from rest, the initial acceleration must have the same sign as the first nonzero velocity and the first nonzero displacement. You can see this by considering a velocity-time graph. Thereafter, the acceleration may change sign, making it, for a while at least, opposite in sign to the velocity.
 

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