MadSci Network: Physics |
This is actually a homework problem in "Advanced Mathematical Methods for Scientists and Engineers" by Carl Bender and Steven Orszag. It turns out that an object rotated about its "middle" moment of inertia will wobble in its rotation (this is called an Eulerian wobble). We can define three axes of rotation for a hammer. The x-axis will be along the handle. The z-axis will be the vertical axis if the hammer is laid flat. The y-axis is from the head to the claw. The moment of inertia is greatest about the z-axis and least about the x-axis. The wobble will not occur when the hammer is tossed about either of these axes, but it will when it rotates about the y-axis. This phenomenon could also be demostrated with a book or a brick. I'm not sure that I can answer the question "why" except to say that the wobble is predicted by the equation of motion (Euler's equation).