Final answer:
The question seems to be asking for the angular acceleration of an object, likely a yo-yo, given a linear acceleration. However, to calculate angular acceleration, the radius of the yo-yo is needed, which is not provided. Without this information, we cannot provide the angular acceleration.
Step-by-step explanation:
Angular Acceleration and Linear Speed Connection
The problem described suggests a scenario where a student is trying to determine the angular acceleration of a yo-yo with a given linear acceleration. Referring to the information provided, we see examples of how linear and rotational quantities are connected, and we understand that the angular acceleration can be determined by understanding this relationship. Unfortunately, the original question is missing some key details that are necessary to make a precise calculation – specifically, we need to know the radius of the object the string is attached to (the yo-yo) in order to convert from linear to angular acceleration.
The idea is to apply the formula α = a/r, where α is the angular acceleration, a is the linear acceleration, and r is the radius. If the radius were provided, and given that the linear acceleration is 1.50 m/s², we could simply divide the linear acceleration by the radius to find the angular acceleration. Without the radius value, however, it is not possible to provide the rate at which the angle is changing when 140 feet of string is out.