The general case requires the use of calculus which we will discuss at the bottom of this page. If the mass is uniformly distributed, the problem is greatly simplified. If the object has a line or plane of symmetry , the cg lies on the line of symmetry.
For a solid block of uniform material, the center of gravity is simply at the average location of the physical dimensions. For a rectangular block, 50 X 20 X 10, the center of gravity is at the point 25,10, 5. There are tables of the location of the center of gravity for many simple shapes in math and science books. The tables were generated by using the equation from calculus shown on the slide.
For a general shaped object, there is a simple mechanical way to determine the center of gravity:. If we just balance the object using a string or an edge, the point at which the object is balanced is the center of gravity. The simplest concept is to use a load cell system. The object is placed on a fixed platform connected to three load cells. The weighted average of each load cell reading gives the location of the center of gravity of the object. A different concept is used where high accuracy is required.
The object is placed on top of a table that is pivoted about a defined axis. The moment due to center of gravity offset of the object from the center axis is measured using a force transducer. The location of center of gravity is derived from the moment measurement by applying the following formula:.
This moment measurement method is used in the KSR and SE series of center of gravity measurement instruments. Depending on what you are trying to do, your requirement for accuracy will vary. For example, if you want to stack books on a table, you only need to know the center of gravity within a few inches.
Centre of gravity coincides with centre of mass, if g is constant. But for large objects g will vary, hence centre of gravity does not coincide with centre of mass. Importance of Centre of Gravity 1. Centre of gravity vastly simplifies calculations involving gravitation and dynamics to be able to treat the mass of an object as if it is concentrated at one point.
The center of gravity is based on weight, whereas the center of mass is based on mass. So, when the gravitational field across an object is uniform, the two are identical. However, when the object enters a spatially-varying gravitational field, the COG will move closer to regions of the object in a stronger field, whereas the COM is unmoved.
If you try to tie your shoes without bending over or without lowering your center of gravity, you might tip over. But if you do lower your center of gravity you should be more balanced and be able to tie your shoes without any trouble.
The best thing we can do in terms of our center of gravity is be aware of where it is and then to use it to our advantage.
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