What is stability?
Center of mass, center of support play with shampoo bottles in water. Define upright, then identify righting moment by speed of return. Add steel rods, experiment.
Diagram. Center of buoyancy = center of support. Center of mass below center of support = positive righting moment. Center of mass above center of support = negative righting moment. Righting moment is the horizontal distance between center of mass and center of support.
Stability is the tendency to return when disturbed. Must disturb something to check for stability. Center of support above center of mass is stable. Balance is something that is locally stable. Center of mass above the center of support, but with a positive righting moment.
How do you get a positive righting moment in a balanced system? If the center of mass is above the bounding area of the base, then it the system is balanced. A disturbance from settled position is met with a restoring force.
How do we find the center of mass?
Cut out shapes in cardboard. Hang with a plumb line to get center of mass.
Cut out pairs of shapes in cardboard. Tape washers inside, seal up the pair, give to another group to find center of mass.
[design and print] Freestanding shapes with mass slugs. Find the center of mass by above method, then predict the stable orientations. Diagram horizontal extent of support, center of mass.
Half circles are equivalent to hemispheres in this use case, because the tangent contact point necessarily lies on a diametrical cross section plane.
How do you get any stability at all if the contact is a single point, the tangency of a sphere to a plane? Answer: with real objects made of real atoms it’s not really a single point. [design and print] Half circles: Successive approximation from few lobes to many lobes. Real objects are always rough, even if only at the molecular scale.
Adding stuff on top. Add structures, find the new center of mass.
Using Solidworks to find the center of mass. [design and screen capture].