How Does a Spool's Acceleration Relate to Force and Mass?

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The discussion revolves around the physics of a spool unwinding under a constant force, with a focus on deriving the acceleration of its center of mass. The user attempts to relate torque, moment of inertia, and angular acceleration but struggles with the friction force involved. A suggestion is made to apply Newton's second law to the spool to create an additional equation that could help eliminate the friction force from the calculations. The goal is to demonstrate that the acceleration of the center of mass is 4F/3M. The conversation emphasizes the importance of understanding the relationship between force, mass, and acceleration in rotational dynamics.
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Homework Statement


A spool of wire mass M and radius R is unwound under a constant force F. Assuming the spool is a uniform solid cylinder that doesn't slip, show that the acceleration of center of mass is 4F/3M


Homework Equations


\tau = I\alpha = F*R


The Attempt at a Solution



Here's what I got, not sure if this is right.
\tau_{}net = \tauF - \tauFfric
I\alpha = F*R - Ffric*R
.5MR^2(a_{cm}/R) = F*R - Ffric*R

a_{cm} = (F-Ffric)/.5M

The problem is that I don't know Ffric (Friction force).

Thank you in advance for help
 
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Use F = ma on the spool to get another equation, this should allow you to eliminate F_fric.
 
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