To measure forward acceleration using a free-swinging ball on a string, one must consider the forces acting on the ball, including gravitational force and tension in the rope. A free body diagram can help visualize these forces. By applying Newton's second law, the net force can be computed vectorially. The relationship between acceleration (a) and the angle (theta) of the string with the vertical can be expressed as tan(theta) = a/g. This equation confirms the connection between the angle and the acceleration due to gravity.
