Interesting Links (example problem):
Just as for systems that are in equilibrium, a large carefully done free body diagram is essential. Be sure to show the directions you're choosing as positive. Don't hesitate to choose coordinate axes that are not the usual horizontal and vertical. If you have an incline, it's often easier to choose axes parallel and perpendicular to the incline.
These problems all involve accelerations. When two bodies are connected by a cord, you can draw two free body diagrams - in fact, you must if you want the tension in the cord. (You can draw a third free body - one of the whole system, but that isn't always as useful.) When you write Newton's Second Law for each, choose the direction of the acceleration as positive. If you merely choose any set of axes as positive for each body, you can have contradictory accelerations. The examples will explain this in more detail.
You will assume that pulleys are frictionless and massless, so that their only effects are to change the directions of the forces. You will also assume for this module that all bodies are essentially points, thus removing any possibility of torques. The alternative to particles (point bodies) is rigid bodies. Those will be discussed in a later module.
Example 1: A body on an incline
Example 2: Two masses and a pulley
Example 3: Two masses; two different inclines
Example 4: A strange cart