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pierce15
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Are there any realistic scenarios for which center of mass is not almost exactly equivalent to the c.o.g., i.e. they must be treated separately?
I don't really understand this. If it is possible to say the CG depends on reference point, then isn't it equally as valid to say the CM depends on reference point? Like for example, if we say "the CG due to only gravity caused by the moon" then we could also say "the CM due to only mass of the moon"sophiecentaur said:CM is always the same. CG depends upon your reference point
The center of mass is the point at which an object's mass is evenly distributed, while the center of gravity is the point at which the force of gravity acts upon an object. In a uniform gravitational field, the center of mass and center of gravity will be the same point. However, in non-uniform fields or when considering objects with varying densities, the two points may differ.
The center of mass is calculated by taking the weighted average of the positions of all the particles that make up an object. This means that the mass of each particle is multiplied by its distance from a chosen reference point, and the sum of these values is divided by the total mass of the object.
The center of gravity is determined by the distribution of mass within an object, as well as the gravitational field in which it is located. On Earth, the center of gravity is closer to the center of the planet due to its relatively uniform density. However, on other planets with different densities or non-uniform gravitational fields, the center of gravity may be located at different points within the object.
The center of mass and center of gravity are important for understanding how objects move and interact with their surroundings. They are also crucial for determining an object's stability and balance. In addition, these points are used in engineering and design to ensure that structures and machines are properly balanced and can safely support their own weight.
No, an object can only have one center of mass and one center of gravity. However, in some cases, an object may have multiple points that can be considered as its center of mass or gravity, depending on the reference point used. For example, a ring-shaped object may have multiple points where its mass is evenly distributed, but the overall center of mass and gravity will still be at the center of the ring.