Final answer:
To calculate work done on a multi-dimensional moving system, it's divided into one-way, one-dimensional segments, utilizing the independence of motion and computed like linear motion.
Step-by-step explanation:
To calculate the work done on a system that undergoes complex motion, such as motion in more than one dimension, a useful strategy involves dividing the motion into simpler, one-dimensional segments. For instance, if an object is moving in two or three dimensions, you can separate the motion into horizontal and vertical components—or in the case of three-dimensional motion, also include the depth component. By doing so, you tap into the principle of independence of motion, where each one-way segment can be analyzed individually without affecting the others.
Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. When an object moves in multiple dimensions, you can find the work done over each one-way, one-dimensional segment and sum them all up to get the total work done.
This approach is very similar to how we approach rotational motion; important aspects of rotational motion correspond to those already defined for linear motion. Essentially, methods for calculating work in linear motion can be applied in a similar fashion to rotational scenarios, as long as the motion is divided properly into one-dimensional segments.