What is the downward acceleration?

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Homework Help Overview

The discussion revolves around the dynamics of a yoyo, specifically focusing on its downward acceleration as it unwinds from a fixed string. The subject area includes concepts from rotational motion and forces acting on rigid bodies.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss applying Newton's second law to both translational and rotational motion, considering forces and torques acting on the yoyo. There are attempts to derive expressions for acceleration based on mass and radius, as well as questions about the dynamics of a slipping cylinder on a ramp and the role of kinetic friction.

Discussion Status

Some participants have provided mathematical expressions related to the yoyo's acceleration, while others are exploring the implications of these equations. There is ongoing inquiry regarding the acceleration of a slipping cylinder, indicating a productive exploration of related concepts.

Contextual Notes

Participants are navigating the complexities of rotational dynamics and friction, with specific attention to the assumptions made about the yoyo's structure and the conditions of the slipping cylinder scenario.

deanwudean
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A yoyo consists of aunfirom disk with a string wound around the rim. the upper end of the string is held fixed. the yoyo unwinds as it drops. what is the downward acceleration?

I got the idea that Inertia*acceleration=force on the rim.
 
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Consider the forces acting on the disk and the torques they produce. Apply Newton's 2nd law to both translational and rotational motion.
 
I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?
 
deanwudean said:
I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)
If the yo-yo is just a uniform disk with the string wound around the rim, this answer can be simplified.

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?
Just add the friction force to the mix. It equals [itex]\mu N[/itex].
 

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