Hammertime

Last Friday, Steve and I went to see the movie Thor.  It was a lot of fun, but Steve keeps insisting the movie was about physics, so I figured I should do a post on it.

One of Thor's powers is that he can use his hammer, Mjöllnir, to fly.  He does this by essentially throwing the hammer, but not letting go, so that it carries him along with it.  My first instinct was that this wouldn't work, but I figured I should go through the mechanics, just to be sure.  Let's say he holds the hammer at his side, and swings it up in a circular arc until it's above his head.  He'll be able to accelerate it until it's straight in front of him, but after this point it will begin to lift him.  Lets say at this point it's moving at a velocity v.  If the hammer has mass m and Thor's arm is of length r, then the force required to maintain it's circular motion is

Once the hammer reaches this point, Thor won't be able to add more energy to it, so let's look at what happens after this.  The lifting force from the hammer will be

where θ is the angle of Thor's arm above horizontal.  If Thor's mass is M, then his upward acceleration will be

θ is a function of time, so we can put it in terms of other variables we have.

Integrating this over the arc will give the velocity of Thor when he finishes the swing.

or a kinetic energy of

That means he could rise to a height of

To get an idea of what this means, let's get some numbers. We'll assume Thor has an average weight of 70 kg.  A quick search for sledgehammers shows a typical weight is about 7 kg.  It's a little tougher to figure out the speed.  I searched around a bit for info, but the best I came up with was this video of a guy swinging a club of similar weight.  He manages about 1 round per second, which translates to a velocity of about 6 m/s.  Thor's a god, so let's estimate he can manage more than double this, and call it 15 m/s.  Plugging all this in gives h = 11.5 cm.  Of course, if we assume Thor has truly god-like strength, then he can swing Mjöllnir as fast as he wants, or we could assume Mjöllnir is stunningly heavy.  Either way, he could manage flight, but it's certainly outside the abilities of any human.

There was one physics detail that really bugged me in the movie.  For much of the film, Mjöllnir is wedged in the ground out in some desert, with a government research team surrounding it.  Occasionally, the team's computers flicker, which they explain is the result of powerful electromagnetic energy being released by the hammer.  What bugs me is that none of them think to simply erect a Faraday cage around it.  Faraday cages absorb electromagnetic waves, and are often used in labs to protect equipment from volatile experiments.  Swarthmore's plasma physics lab uses one to protect their computers from the powerful waves emitted by their spheromak.  You may think I'm being petty, but I feel strongly that if a movie is actually going to talk about science, they should get it right.