Do you have to *do* the experiment, or just design it? In theory it's pretty simple but it might rely on some quick stopwatch-fu.
The most basic way is to measure its time taken to roll down a ramp. In general, objects with a higher moment of inertia relative to their mass (eg. hollow tubes) will accelerate more slowly down the ramp than objects with a low one (eg. spheres). This is because it takes more torque to make them spin, and the speed of their spin is directly related to the speed they roll down the ramp.
At a first look, I = (m*r^2*t^2/2d)*(g*sin (p)-2*d/t^2)
where r is the radius of the object,
p is the angle of the ramp,
t is the time taken to roll a distance d along the ramp.
You should be able to check this for yourself with a force balance on a ball on a ramp, taking into account a force from the ramp on the sphere pointing up the ramp which induces the angular acceleration. DISCLAIMER I haven't checked this so thoroughly - the principle is right but no guarantees on the math.
EDIT with better maths.
Other experiments to measure this will generally involve the same principle - applying a force which causes the object to both spin and accelerate in a direction, then measuring its linear acceleration and using it to calculate the angular.