Thor’s mechanism for flight is pretty straight forward all things considered. Thor’s standing around, minding his own business wishing he was flying. He starts spinning Mjölnir around in a circle. Then, once it’s going pretty quickly, he lets it fling forward. He holds on tight and flyies behind it. So it’s not really flying as much as it is a strange mechanism for throwing himself great distances but hey, it’s a lot cooler than the way I fly around. Anyway, what’s convenient for us is that we can use the Law of Conservation of Momentum to figure out how quickly he has to spin the hammer for this to work. So what do we know about momentum? Well, momentum is the product of mass and velocity. So something that has a lot of momentum either very massive, is moving very quickly, or some of both. Those two numbers then, mass and velocity, are all we really need to get started on this problem. Well if we assume the value from the trading card, then we know that the hammer is 19.2 kilograms and Thor himself, according to the Marvel wiki website, weighs 291 kilograms (or 640 pounds, all muscle I would assume, being a god and all). The only other thing we need is his flight speed, which the Thor Fansite lists at around 11265 meters per second. With these numbers in hand we can calculate the momentum of Thor and Mjölnir in flight. We find that the momentum of the Thor-Mjölnir system is p=mv p=(291 kg+19.2 kg)(11265 m/s) p=3.5 x 106 Newton seconds So you may very well be asking yourself why this is a useful thing to know at all. I mean, a Newton is already kind of an arbitrary unit of measurement in our everyday life. A Newton second is even more so- what does that even mean? But while this may not make much intuitive sense to us on a day-to-day sort of level, it is still a very helpful tool. That’s because momentum is conserved! What does that mean? It means that the amount of momentum we have at the end of a thing (to pick an example at random, flying to strike Justice somewhere), has to be the same as the amount of momentum at the beginning of that thing. While in flight, Thor and Mjölnir have the same speed. That’s why we’re able to write the formula the way we did above, combining the masses. But in a scenario where they have different speeds- like preflight when Mjölnir is moving in a circle but Thor is stationary- we need to take into account that speed difference. Therefore we would write p=m1v1+m2v2 So let’s take into account all of the things we know. We know the momentum of Thor and the hammer when they are flying. We know that the momentum when they are flying has to be the same as the momentum when Thor is swinging the hammer, preparing to fly. We know that Thor’s velocity when he is preparing to fly is 0 meters per second. Therefore, we can easily calculate the velocity of the hammer before take off. One caveat before we do this though. The number we get will be the linear velocity, not the angular velocity. Since we are using the linear momentum (since Thor flies in a straight line path) we have to use it to calculate the linear velocity. The actual number we are interested in is the angular velocity (since the hammer spins in a circle before flight). Don’t worry though, we can use one number to find the other pretty quickly. Setting up an equation, based on the conservation of momentum, that capitalizes on everything we know, to find the velocity of Thor’s mighty hammer Mjölnir before takeoff looks something like this p1=p2 3.5 x 106 Newton seconds=m1v1+m2v2 3.5 x 106 Newton seconds=(291 kg)(0 m/s)+(19.2 kg)v2 3.5 x 106 Newton seconds=(19.2 kg)v2 v2=182,292 m/s So that’s a woppingly fast 182,292 meters per second. But wait, that’s not all. As we mentioned earlier, that’s the linear momentum. The velocity that we are interested in, how quickly the hammer is moving around in a circle, is the angular velocity. The two have a close relationship though. Line B is tangent to Circle O The linear velocity has a path that looks like Line B. The angular velocity has a path that looks like the outside of Circle O. At any particular moment, an object moving around the path of Circle O could start moving along the path of Line B. If Thor were to throw his hammer rather than hold onto it to fly, it would have a velocity of 182,292 meters per second in a straight line. But that is not the velocity it has in the circular path. To get that, we must divide the linear velocity by the radius of the circle. What is the radius of our circle? Well, the circle is the hammer spinning around Thor’s hand right? So the radius would be the length of the handle which our trading card tells us is 22.7 inches or 0.5766 meters. Now we are finally ready to answer the question. Using the linear velocity and the radius, we calculate the angular velocity of the hammer v=rw v/r=w (182,292)/(0.5766)=w w=316,150 m/s So to achieve flight, Thor has to spin his hammer at 316,150 meters per second. That’s an astonishingly high speed. In fact, it’s 1.055% the speed of light. That might not seem like a very high percentage, but remember what it says. The speed that Thor has to spin his hammer around in a circle to fly is one one-hundredth the speed that light moves. More questions about one of our favorite heroes answered with physics. Unfortunately, if the trailer is anything to go off of, we won’t be able to remember any of this when we go to see Thor: The Dark World, because we’ll be too busy having our minds blown by how awesome it is. Next time, we’ll break down something that flies: either more on Thor, or Iron Man 3, or Star Trek. Leave your votes in the comments. It’ll help me decide. Thanks for reading and we’ll see everybody next time!
Posted on: Sun, 01 Sep 2013 13:10:10 +0000