a. An irregularly sharped wooden block is suspended from various points, and a plumb line is dropped to determine the center of gravity.
b. A double cone will roll up an incline. (Actually the axis or c.m. of the cone descends because of the divergence of the rails.)
c. The leaning tower is unstable with the top in place, but stable when the top is removed.
d. Hold your belt up with an otherwise unstable plastic bird.
e. A dumbbell with unequal masses on the end of a rod is suspended by s string to locate the center of mass. The dumbbell can then be tossed across the lecture hall to show that the center of mass follows a parabola, even though the ends are flying around. The center of mass is marked with phosphorescent paint which can be activated by ultraviolet light. Then in total darkness the students can see the dimly marked center of mass flying across the room in a parabola.
This oloid is composed of two circular disks which roll in such a way that the center of gravity stays constant.
If a series of identical rectangular blocks is stacked out at their balancing points from the top down, the top block can stick out arbitrarily far. You can show with a simple center of mass calculation the total "stick-out" distance; that is, the horizontal distance from the back of the bottom block to the back of the top block is 1/2(1 + 1/2 + 1/3 + 1/4 + ...). This series grows without limit.
Many students are surprised to see the top block "sticking out in space", no part of it over the bottom block of the stack. The series above shows that this can happen with a stack of only 6 blocks. In practice at least 6 are needed, and several more to make to effect dramatic.
This graphic demonstration of stability comes from Russia. When the line of the plumb bob hanging below the center of mass falls within the base, the prism is stable. But when the extended plumb bob line falls outside the base, the prism tips over. This demonstration is similar to the Tower of Pisa [1], and the two can be used together.
"Glasnost gives us this pretty demonstration from Russia. In Russia all students are required to take 5 years of physics, and these demonstrations are used throughout Russia. However, the Russians lost the Cold War so, though it pains me to say it, perhaps it is better to watch MTV than to study physics too hard!"
A beautiful wine rack demonstrates how, for stability, the center of mass must be over the support base.
Links:
[1] https://demoweb.physics.ucla.edu/node/391