Playing partner ran over my ball with a cart on #18 fairway. I'm pretty sure I get free relief, but I want to know what the specific rules are.
This is covered by Rule #9.6 - Ball Lifted or Moved by Outside Influence. In Stroke play, another player is an outside influence. If it was match play, and my opponent moved the ball (intentionally), then they get a one-stroke penalty (Rule #9.5). If I moved it, or my caddie moved it (intentionally), then I get a one-stroke penalty (Rule #9.4). And then the ball must be replaced. If it's an accident, then the ball must be replaced, but there is no penalty.
Rule #14.2 covers replacing the ball. You have to place it on the original spot, or, if you don't the exact spot, then it must be estimated. My situation specifically relied on Rule #14.2-d(2). The original spot was known, but I could not replace it there because the lie would be altered. So I get a club length, and I have to stay in the general area.
Rule #14.2 also covers the scenario when you need to lift your ball in a bunker to identify it. You need to recreate the lie that you previously had, or you would receive the general penalty (two strokes).