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## Homework Statement

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A solid cylinder of mass m and radius r lies flat on frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The circumference of the cylinder is sufficiently rough so that the string does not slip with respect to it. What is the acceleration of the mass m attached to the end of the string?

## Homework Equations

Torque formula:

[itex]rT-rF = I\alpha = mr^2\alpha/2[/itex]

[itex]T-F = mr\alpha/2[/itex]

where [itex]\alpha[/itex] is angular acceleration.

acceleration of center-of-mass formula for cylinder:

[itex]a_{cm-of-cylinder} = (T+F)/m[/itex]

Formula that describes tangential velocity for upper string and lower string (that I am not really sure of):

[itex]v_{cm}+r\omega[/itex] or [itex]v_{cm}-r\omega[/itex]

## The Attempt at a Solution

What I tried is differentiating the last formula above and using that as tangential acceleration formula, and get the solution using all the three formula. But I reached a wrong answer. The answer is [itex]-T/4m[/itex].