What it shows:

A suspended hula hoop has the same period of oscillation as a pendulum whose length is equal to the diameter of the hoop.

How it works:

The parallel-axis theorem allows us to readily deduce the rotational inertia of a hoop about an axis that passes through its circumference and is given by

^{\(I = I_{cm} + MR^2 = 2MR^2\)}

where M is the mass of the hoop and R is its radius. The period of oscillation thus becomes

\(T = 2\pi \sqrt{I\over mgd} = 2\pi \sqrt{2MR^2 \over Mg(R)} = 2\pi \sqrt{2R\over g}\)

which is equal to that of a pendulum whose length is \(2R\), or the diameter of the hoop.

Setting it up:

A length of aluminum angle, C-clamped to the edge of the lecture bench, provides a simple suspension mechanism for the hula hoop and pendulum. Since we're only comparing the period of oscillations of the two, no timer is required unless you wish to quantitatively predict the period.

Comments:

Simple calculations and simple experiment that shows off the power of the parallel-axis theorem.