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## Homework Statement

A yo-yo is made from two uniform disks, each with mass m and radius R, connected by a light axle of radius b. A light, thin string is wound several times around the axle and then held stationary while the yo-yo is released from rest, dropping as the string unwinds. Find the linear acceleration of the yo-yo.

## Homework Equations

[itex]

\tau=TR=I\alpha[/itex]

[itex]

F=ma[/itex]

## The Attempt at a Solution

[itex]\tau=TR=I\alpha[/itex]

[itex]Tb=2\left(\frac{1}{2}mR^2\right)\alpha[/itex]

since [itex]a_{tan}=r\alpha[/itex],substituted into the equation above and simplified,

[itex]

Tb=mRa[/itex] ...1

The yo-yo is accelerating downwards linearly, so

[itex]

2mg-T=2ma[/itex] ...2

Solving for T in eq.1 and substituting into eq.2,

[itex]

2mg-\frac{mRa}{b}=2ma[/itex]

Solving for a, I got

[itex]

a=\frac{2g}{2+R/b}[/itex]

which is not the right answer... the correct answer is

[itex]

a=\frac{2g}{2+(R/b)^2}[/itex]

what did I do wrong??