What Is the Tension of the String in Yo-Yo Motion?

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SUMMARY

The discussion focuses on the tension of the string in a yo-yo motion scenario involving two uniform discs, each with mass M and radius R, connected by a light axle of radius a. The equation of motion derived using conservation of energy is x'' = (2a²g)/(2a² + R²), while the tension in the string when the center of mass has fallen a distance y is calculated as T = (2MgR²)/(2a² + R²). The participant questions the necessity of specifying the tension at a distance y, suggesting a misunderstanding of the uniformity of tension in the system.

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  • Understanding of classical mechanics principles, particularly conservation of energy.
  • Familiarity with the dynamics of rotational motion and torque.
  • Knowledge of the properties of uniform discs and their mass distribution.
  • Basic proficiency in solving differential equations related to motion.
NEXT STEPS
  • Study the principles of conservation of energy in mechanical systems.
  • Explore the dynamics of rotational motion, focusing on torque and angular acceleration.
  • Investigate the effects of mass distribution on tension in strings and cables.
  • Learn about differential equations in the context of motion analysis.
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jasony
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Homework Statement


A yo-yo consists of two uniform heavy discs, each of mass M and radius R, connected
by a light axle of radius a around which one end of a string is wound. One end of the string is attached to the axle and the other to a fixed point P. The yo-yo is held with its centre of mass vertically below P and then released.

Homework Equations


Assuming that the unwound part of the string is approximately vertical, use the principle of conservation of energy to find the equation of motion of the centre of mass of yo-yo. What is the tension of the string when the centre of mass has fallen a distance y?

The Attempt at a Solution


I just want to check if my answer is correct.
My answers are x''=(2a^2g)/(2a^2+R^2) for the equation of motion
and T=2MgR^2/(2a^2+R^2)

Thanks
 
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That's what I get.
But why does the question ask for the tension at a distance y? Surely the tension is the same everywhere? Or have I gone wrong somewhere?
 

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