Yo-yo problem - rotational motion

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Homework Help Overview

The problem involves a yo-yo with specified dimensions and mass, focusing on its motion as it falls a certain distance. The questions pertain to the speed of the yo-yo, the tension in the string, and the acceleration of its center of mass during the fall, all within the context of rotational motion and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using energy conservation to analyze the problem, considering both rotational and translational energy. There is uncertainty about converting height into rotational displacement and how to relate the different forms of energy. Questions arise regarding the appropriate moment of inertia to use and the interpretation of the height in terms of potential energy.

Discussion Status

The discussion is active, with participants exploring various approaches to the problem. Some guidance has been offered regarding the use of energy conservation and the relationship between rotational and translational motion. However, there is no explicit consensus on the method or the details of the calculations.

Contextual Notes

Participants are navigating assumptions about the moment of inertia based on the yo-yo's dimensions and the height from which it falls. There is also a focus on ensuring the correct interpretation of the physical parameters involved in the problem.

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Homework Statement



consider a yo-yo with R = 3.3 cm, r = 0.3 cm, and mass m = 84 g.

What is the speed of the yo-yo after it has fallen a distance h = 1.20 m?

What is the tension in the string while the yo-yo falls?

What is the magnitude of the acceleration of the centre of mass as the yo-yo falls?

Homework Equations



L = Iw
I = 0.5MR^2
KEr = 0.5Iw^2
Tnet = Ia

The Attempt at a Solution



change h into rotational displacement, not sure where to go or if that's even right.

can anyone give me direction?
 
Last edited:
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would you solve this using conversation of energy?
 
Yes, I would use energy for the first part. You have both rotational and translational energy and they are related by v = rω. The r = 0.3 cm must be the radius of the center "axel" that the string unwraps from.

If you don't put in the h = 1.2 too soon, you'll have the speed as a function of h. Perhaps you can differentiate that with respect to time and get something you can use to find the acceleration.
 
what would the moment of inertia be? 0.5mr^2, would you use the large or small radius?

would the height be 1.2 m? for PE
 
Yes, the large radius for moment of inertia.
Yes, the initial height is 1.2 m.
 

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