Rotational Inertia equation help

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SUMMARY

The discussion focuses on deriving the equation for the linear acceleration of a mass m that is suspended from a uniform disk of mass M and radius R, which rotates without friction. The key equations involved are a = rα (where a is linear acceleration and α is angular acceleration) and Torque = inertia * angular acceleration. The confusion arises from the interaction of gravitational force and the rotational dynamics of the disk, indicating that the system is not in free fall due to the tension in the string affecting the acceleration of mass m.

PREREQUISITES
  • Understanding of rotational dynamics and torque
  • Familiarity with the concepts of linear and angular acceleration
  • Knowledge of moment of inertia
  • Basic principles of forces acting on a system
NEXT STEPS
  • Study the derivation of the moment of inertia for a uniform disk
  • Learn about the relationship between linear and angular motion in rotational systems
  • Explore the concept of tension in strings and its effect on acceleration
  • Investigate the application of Newton's second law in rotational dynamics
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Homework Statement



Derive the equation for the linear acceleration of a falling mass m suspended by a string from the rim of a uniform disk of mass M and radius R that is free to rotate without friction about its principal axis.

Homework Equations



a=rα
linear acceleration = radius*angular acceleration

Torque=inertia*angular acceleration

The Attempt at a Solution



I don't really understand the question. If something is in free-fall, isn't its acceleration g? I just don't understand where the variables for the masses go. Any help is appreciated..
 
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