For many climbers, the technique and trade craft on the rock is meant to ensure your safety, and that of your group/team as well. But it usually doesn’t go past that. The actual physics of your gear and it’s efforts to save your life should you fall is quit intriguing. For example,
Fall factor is a measure of how big a climbing fall is. To be precise it is the ratio of distance fallen divided by the length of rope available to absorb the fall. This fall factor is what determines how much force is placed on the rope and accompanying gear. With normal single pitch climbing, people rarely generate large fall factors. They are perhaps around 0.2 or smaller, and this sort of fall may produce 3-4kN of force. But on a multi-pitch you can have the potential case where the first climber advances and falls before they can place a piece of gear into the rock. They would then fall down past their belayer (partner giving and taking rope) and the same distance again; this would be a fall factor 2. Such falls can produce tremendous amounts of force even though the total distance fallen can be relatively small, it is falls like this that can snap ropes and yank bolts or gear out of the rock – some of the worst case scenarios for climbers.
THIS article from The Guardian is a short and extremely topical text on the physics of climbing (well, falling in this case). The above text (from the article) is a good layman’s overview. Think you’re decent with physics and associated equations? Here is a more detailed look at the fall factor. And apparently MIT did in fact teach a Physics of Rock Climbing class, though this page doesn’t indicate whether it’s still taught (since it’s dated 2006).