I have a physics test coming up in a couple of days and I really need to have some things explained to me. It is about something that I think is called in english "the velocity of the center of gravity" or something a long those lines. I have not been able to find anything anywhere about this so that is why I am here. In my physics book they roughly show the following: 
Sorry if the picture is somewhat unclear/poor resolution, but this is the best i could do when remaking it in paint. After having showed this derivation they mention something about the constant velocity of the center of gravity and stuff. To be honest i don't quite understand what they are doing here, what this means or what implications/uses you can have from this. Since my book does a poor job of explaining this, could anyone tell me what is going on in this picture, what this whole constant velocity of the center of gravity is and what uses you have from this/what it means. Illustrations with pictures, not too complicated answers and not too complicated physics language would be very much appreciated since I am only 18 years old. Any cool but not too complicated ways to calculate things with this would also be awesome if someone wants to provide it. I apologize beforehand for the language in this text, as english is not my first language. Would be happy to get answers asap!
2 Answers
The laws of motion apply to point particles, or to extended rigid bodies at the center of mass. Just as a particle without a (net) force acting on it will move with constant velocity, so does an extended rigid body without a (net) force will have its center of mass move with constant velocity.
If you apply a force to an object AND you do not want to put a torque on that object, then you must apply that force to that object’s center of gravity.
(Conservation of the velocity of the center of gravity: to add/subtract to the translational velocity of an object, you must apply a net force to that object’s center of gravity. Think Newton's First Law of Motion.)
2. Use the center of mass of an object to calculate its momentum, not its center of gravity.
(Conservation of momentum.)
3. If your universe has only one object, then its center of gravity is at the same point as its center of mass.
4. If your universe has more than one object, then the center of gravity of an object is not at the same point as the center of mass of that object without making assumptions.
5. Any point object has a center of mass at the same spot as its center of gravity - at that point.
