Acceleration and Friction of a Rolling Cylinder

AI Thread Summary
To find the acceleration of a lawn roller modeled as a thin-walled hollow cylinder, the relationship between friction, force, and acceleration must be established. The equations indicate that the friction force is equal to Ma, where M is the mass and a is the acceleration. However, confusion arises when substituting this back into the force equation, leading to the equation F - ma = ma. The user seeks clarification on the correct approach to solve for acceleration and friction without encountering contradictions. Understanding the relationship between linear and angular acceleration is crucial for resolving the problem correctly.
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Homework Statement


A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle.

a)If it rolls without slipping, find the acceleration.

b)If it rolls without slipping, find the friction force.

Homework Equations


I_{Hollow Cylinder} = MR^{2}

\sum \tau = f_{friction}R = I\alpha = MR^{2}\alpha

\sum F = F - f_{friction} = F = Ma

The Attempt at a Solution


I'm really not sure...it seems like I have too many unknowns (R, a, alpha, friction)
 
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Ok, so I just remembered that because its not slipping, I can change \alpha to \frac{a}{r}

so I get f_{friction}R = MR^{2}*\frac{a}{R}

which cancels down to f_{friction} = Ma

But when I plug that back into the other equation I just get F - ma = ma...

where did I go wrong?
 
Any help, guys?
 

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