"Solve Problem $3$ from Exam $2$ using the following values: mA $=11\mathrm{.}4[$kg$]$ mB $=8\mathrm{.}5[$kg$]$ mpulley $=6\mathrm{.}4[$kg$]$ r $=0\mathrm{.}2[$m$]$ T $=10[$N$*$m$]$ With these conditions, calculate the acceleration of cylinder A $[$m$/$s$2].$ A positive number represents an upward acceleration. Report your answer to three significant figures."

Two cylinders are connected via a rope that passes over a pulley. The cylinders have masses of $m_A$ and $m_B,$ and the pulley $($model this as a thin disk$)$ has radius $r$ and mass $m_{\text{p}\text{u}\text{l}\text{l}\text{e}\text{y}\text{.}}.$ The system starts from rest, and a constant torque T is applied to the pulley. A positive torque is counterclockwise, and a negative torque is clockwise. The rope does not slip on the pulley.

Calculate:

Determine the linear acceleration of cylinder A$,$ noting that positive values are upward, and negative vales are downward.

Tips:

This is very similar to the example and homework, except the torque will need to be included in your SUM of moments equation.

Check the direction of rotation using statics. If the applied torque is positive $($counterclockwise$)$ and greater than the static torque caused by the masses, then the pulley will accelerate in the counterclockwise direction.