In physics, the center of gravity (CoG) of an object is the average location of its weight. In a uniform gravitational field, it coincides with the object's center of mass. (In modern Britain the spelling centre is standard. Both spellings originated in England; center is now standard in America.)
The concept of center of gravity was first introduced by the ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point __ their center of gravity. In work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of gravity as low as possible. He developed mathematical techniques for finding the centers of gravity of objects of uniform density of various well_defined shapes, in particular a triangle, a hemisphere, and a frustum of a circular paraboloid.
Aeronautical significance
The center of gravity is an important point on an aircraft, as it defines the amount of mass forward or behind the center of gravity that needs to be moved in order to pitch the plane up or down without applying any external forces. In conventional designs the CoG is often located very near the line 1/3rd back from the front of the wing. That is the line where most wings generate their lift, known as the center of pressure (CoP), so by balancing the plane at that point, the lift and weight balance out with no net torque. The CoG is sometimes moved slightly to the rear of this line in order to provide the plane with a natural "nose up" tendency when lift increases (like when applying more power).
If the balance of the plane is moved too far from the CoG, the control surfaces may have trouble controlling the plane. The actual force generated by the surfaces is typically quite small (a few pounds) but due to their location at the end of the tail (typically) they generate considerable torque to pitch the plane. If the CoG starts to move away from the CoP there will be an increasing amount of constant torque they have to counteract, and if it moves too far, it may be more than the controls can counter.
In the case of a loose distribution of masses in free space, such as shot from a shotgun, the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass.
The centre of mass of this figure is at a distance of 8.5 units from the left corner of the figure.
The center of mass is often called the center of gravity because any uniform gravitational field g acts on a system as if the mass M of the system were concentrated at the center of mass R.
The centre of buoyancy, is the centre of gravity of the volume of water which the hull displaces.
The distance between the centre of gravity and the metacentre is called the metacentric height, and is usually between one and two metres.
The righting force on the ship is then caused by gravity pulling down on the hull, effectively acting on its centre of gravity, and the buoyancy pushing the hull upwards; effectively acting along the vertical line passing through the centre of buoyancy and the metacentre above it.
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