Say I have a rectangle of width w and height h centred at (0, 0) on a 2D coordinate plane. The rectangle is free to move on a frictionless medium. It is not attached at any point. Case 1: A single force F = (Fx)i + (Fx)j acts at a point (x, y) How does the rectangle move? I looked it up on some websites and I think that the tangential component of the force rotates the rectangle around it's centre of gravity and the parallel component of the force causes translational motion. Is this correct? Case 2: Multiple forces F1, F2, ..., Fn act on points (x1, y1), (x2, y2), ..., (x3, y3) I have searched everywhere for a solution to this problem but I cannot find it. Is there a way to figure out mathematically how the rectangle rotates and/or translates? Is there a general method to figure out the rotational and translational motion in both cases?