MadSci Network: Physics
Query:

Re: rotating hammer

Area: Physics
Posted By: John Balbach, Grad student Physics, Washington University
Date: Mon Apr 15 11:03:17 1996


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).

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