Final answer:
The question is related to rotational motion in Physics at the College level, where the angular acceleration and the acceleration at a specific point on a cylinder used as a roller need to be found using given linear velocity and acceleration.
Step-by-step explanation:
The subject of this question is Physics, and it appears to be suited for a College level class, likely within a physics course focusing on classical mechanics or specifically rotational motion. The question tasks the student with determining the angular acceleration of a cylinder and the acceleration at a point on the cylinder, given the linear velocity and acceleration of a crate moving on the rollers.
To find the angular acceleration (typically denoted as α), we can use the relationship α = aT / r, where aT is the tangential (linear) acceleration of the crate and r is the radius of the cylinder. Assuming there is no slippage between the cylinders and the crate, the tangential acceleration of the crate will be the same as that of the point on the cylinder's surface.
The acceleration of point A on the center cylinder can be considered as the tangential acceleration, which, as previously stated, is equal to the linear acceleration of the crate, provided there's no slipping.