The use of Newton's second law for rotation involves the
assumption that the axis about which the rotation is taking
place is a principal axis. Since most common rotational problems
involve the rotation of an object about a symmetry axis, the use
of this equation is usually straightforward, because axes of
symmetry are examples of principle axes. A principal axis may be
simply defined as one about which no net torque is needed to
maintain rotation at a constant angular velocity. The issue is
raised here because there are some commonly occurring physical
situations where the axis of rotation is not a principal axis.
For example, if your automobile has a tire which is out of
balance, the axle about which it is rotating is not a principal
axis. Consequently, the tire will tend to wobble, and a periodic
torque must be exerted by the axle of the car to keep it rolling
straight. At certain speeds, this periodic torque may excite a
resonant wobbling frequency, and the tire may begin to wobble
much more violently, vi