Q&A for How to Calculate Center of Gravity

Center of gravity (CG) is very important, especially in aircraft and other vehicles like cars and trains. The Vehicle has to be designed so the CG is within certain limits so the vehicle will be well-balanced while in motion.

Balance it on a knife edge and record the position by marking the edge. Then, turn the object approx. 30 degrees and re-balance it on the knife edge. Record the position by marking the edge -- you should now have 2 intersecting lines, and the intersection point will give you the center of gravity.

It's more useful in certain sports and careers. If you are an engineer, you don't want whatever you're building to be off center. In sports such as gymnastics, it's easier to do harder moves if you know where your center of balance is.

It all comes down to the geometry, so if you have the dimensions and the object is homogenous and homogenous geometry e.g. extrusion, you can easily calculate the CoG. By dividing the shape into the blocks of same size (under mass distribution homogeneity assumption this gives the blocks same weight too), you calculate the CoG position from the weight of the block(that can be set to 1 as they are all equal) and its distance from a datum (distance from a datum set at the corner of the shape, bear in mind you want to use half of the block size as increment of those distances ("local block CoGs")), repeat that for two directions i.e. horizontal and vertical, following the steps in this wikiHow.

You can use force balance (assuming the object is a point mass at the center of gravity, and being sure to include friction) to determine if that object will slip on an incline of a certain angle.

Assuming equal mass distribution, the center of gravity of a circular element is always at its center. If the distribution is uneven, typically the problem will give you enough information to calculate it. Or, if it's a real world scenario, you can always try dangling the object at different points and noting where the lines perpendicular to the ground intersect each other. However, this approach may be unrealistic.

Yes, provided everything in the object is a solid, because liquids and gasses have different types of mechanics because they are different types of matter entirely.