The following two problems concern the same physical situation:

A spool of mass $M=1kg$ sits on its side on a frictionless horizontal surface. A thread wound around the spool is pulled with a force $T=4N$ as shown below. The total moment of inertia about the center of mass of the spool is $I=0\mathrm{.}8kg*m^2,$ its outer radius is $R=1m$ and its inner radius is $r=0\mathrm{.}5m.$ The spool starts from rest.

Top view

$10.$ The magnitude of the angular acceleration, $,$ of the spool is

a$.=T\frac{r+R}{I+M{r}^2}$

b$.=T\frac{R}{\text{I}}$

c$.=T\frac{r}{\text{I}}$

$11.$ The magnitude of the translational acceleration of the center of mass is

a$.a_{cm}=\frac{T}{M}$

b$.a_{cm}=\frac{T}{\text{I}}$

c$.a_{cm}=\frac{T}{I+M}$