Consider a hollow cylinder with a dense 1kg weight affixed to one point on the inside. If placed on an inclined plane, the cylinder will not roll down if there is sufficient friction.
If we gradually reduce the density of the weight toward the volume of the cylinder (edit: alternately, if we advance the cylinder's rotation), there will reach a point where it will begin to roll.
What factors determine this point? I presume it has to do with the center of gravity with respect to the rotating axis?
Edit: This is not homework. I'm a high school dropout. I am considering the construction of a robot that is essentially a heavy box hung between parallel bike wheels on a single axle. I am considering the rollover condition, i.e.: how far can the box tilt before rolling over given a known center of gravity. The box would lean forward if climbing a slope. If the climb is too great, the box would turn too much and roll over. I would limit the tilt with software to prevent a rollover if I knew the limit.
Edit 2: My question is essentially this one, which has been answered: Equilibrium and movement of a cylinder with asymmetric mass centre on an inclined plane
Thanks to commenter below who gave me the correct search terms.
