How does the radius of an object moving in a circular path relate to its acceleration?  If the radius  increases, what happens to the acceleration?

The acceleration of an object moving in a circular path is given by the centripetal acceleration formula, which is a = v^2 / r, where 'a' is the acceleration, 'v' is the velocity (speed) of the object, and 'r' is the radius of the circular path.

From this formula, we can see that the acceleration is inversely proportional to the radius. This means that if the radius increases, the acceleration decreases, assuming the speed of the object remains constant. Conversely, if the radius decreases, the acceleration increases.

So, to answer your question, if the radius of the object's path increases, the acceleration of the object decreases.