Chapter 10 - Section 10.3 - Rotational Inertia and the Analog of Newton’s Law - Example - Page 177: 10.9

$ a = \frac{ mg} {\frac{1}{2}M+m}$

We know the following equations: $ma = mg +( -T) = mg - \frac{1}{2}Ma $ $ I = \frac{1}{2} MR^2 $ $T = \frac{1}{2}Ma$ Solving the first equation for $a$ and combining these, we find: $ a = \frac{ mg} {\frac{1}{2}M+m}$