Rotational Inertia equation help

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The discussion centers on deriving the equation for the linear acceleration of a mass m that is falling while suspended from a rotating disk of mass M and radius R. Participants clarify that the system is not in free fall due to the additional forces acting on it, specifically the tension in the string and the rotational inertia of the disk. The relationship between linear acceleration and angular acceleration is emphasized, along with the role of torque and inertia in the system. Confusion arises regarding the placement of mass variables in the equations. Understanding these dynamics is crucial for solving the problem accurately.
andrewwg94
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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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