The Physics Of A Falling Coffee Cup

On Tuesday this incredible thing happened at work. I didn't think such a thing was possible. The laws of falling bodies would explain it, I'm sure. If I knew more about physics, I could say how and why it happened.

What happened was this: I was talking to my co-worker, and standing behind the public service desk in the library, holding my cup of tea. I was getting ready to make an important point--so perhaps I was starting to wave my hand, I don't know ---but all of a sudden the mug slipped from my fingers, and dropped to the carpeted floor. As I lost hold, I thought, "Oh, this is going to be an absolute disaster. The tea will pour out all over the carpet, and the cup might even break. It will be noisy and there will be a big, embarrassing mess." In a fraction of a second, I thought all of this.

As the cup went down I felt the tea splash onto my black work pants. I stepped back from the point of impact, and looked down, expecting to see spilled tea and possibly cup shards everywhere.

Instead I saw that my coffee cup had made a perfect landing, right-side-up on the carpet, as if it had been carefully placed there. A perfect landing! I was stunned. Other than the tea that had splashed my legs, there was not a drop of tea to be seen anywhere. I couldn't believe it.

I looked around the room. Students had their heads bowed over textbooks; they sat talking to each other. No one had noticed my near-calamity. My cup sat there on the floor quietly, still mostly full. Julie said, "You can still drink it."

I reached down and picked it up. I was so tickled. I couldn't get over the fact that we could just go on with our conversation as if nothing had happened.

It was like being on an episode of Bewitched, and having Samantha twitch everything back into the cup and set it upright. I felt like one of the clueless mortals on the show, who are always rubbing their eyes and swearing off drink, because they see things that defy the laws of physics.

I was so puzzled by how it happened, I visited some physics websites, to see if I could find answers. The cup doesn't have a flexible spine, so it can't re-orient itself like a cat. It is the conservation of angular momentum, by the way, that allows the cat to rotate its body and slow its rate of rotation enough so that it lands on its feet safely. Also, the cat manipulates its moment of inertia, by extending and retracting its legs and rotating its tail, so it can change the speed at which it rotates, which gives it control over which part of its body hits the ground.

But I digress. Obviously, my coffee cup didn't need to re-orient itself anyway, since it slipped out of my hands bottom-first. So the whole issue of the cat is moot. Now here's an interesting question: Do you know which would hit the floor first if dropped together? My cup of tea or a feather?

Well, it depends. If a certified Joy Thief suddenly walked in and sucked all the air out of the room, so that you had a vacuum, you could drop my cup of tea and a feather at the same time, and they would both land together. Why? Because when there is no air resistance, the only force working on the cup and the feather is gravity, and when gravity is the only force, objects accelerate at the same rate.

On Earth, this acceleration value is 9.8 m/s/s. This is such an important value in physics that it is given a special name - the acceleration of gravity - and a special symbol - g.

Now, on the other hand, if a blowhard followed on the heels of the Joy Thief and suddenly filled the room with hot air, so that you no longer had a vacuum, the cup of tea and the feather would fall at different rates. Because now air resistance would be another factor affecting the fall of the objects. The cup would drop faster, because it has more mass, and it takes longer for it to reach a point where there is enough air resistance to balance the downward force of gravity and keep it from accelerating any further. This point, once it is reached, is known as terminal velocity. The feather, having less mass, doesn't have to fall long before it encounters enough air resistance to bring it to terminal velocity --at which point it ceases acceleration.

My thanks to the website "Physics Classroom" for explaining all this to me. It has finally made clear that whole feather vs. stone question, which I never understood before. But of course it doesn't have anything to do with my original question. How did my coffee cup land so straight and true? Shouldn't the impact have made it tip over? My crash course in physics has taught me that you can calculate the impact force of an object by measuring its stopping distance --how far it continues to travel after the impact. But my coffee cup didn't appear to travel at all. Does that mean that the impact force was "0"?

Or maybe the cup bounced straight up, and came down again, and all the liquid poured back in, like in a cartoon. Yeah, that must have been it.

If I go back to my cubicle and drop a cup full of tea, will I get the same result?