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Center of Gravity
*** Shopping-Tip: Center of Gravity
{{Otheruses4|the centre of gravity in physics|the center of gravity as a military concept|Center of gravity (military)}}
{{accuracy}}
{{merge|center of mass}}
In
physics, the '''centre of gravity''' (CG) of an object is a point at which the object's
mass can be assumed, for many purposes, to be concentrated. For example, if you hang an object from a string, the object's centre of gravity will be directly below the string.
The path of an object in
orbit depends only on its centre of gravity. In objects that are radially symmetric, both the center of gravity and the
center of mass coincide.
The centre of gravity of an object is the average location of its weight. In a uniform gravitational field, it coincides with the object's
center of mass.
Note that the center of gravity of a body is ''not'' a point such that the gravitational field due to that body is equal to the gravitational field if all mass were concentrated there. Such a point usually does not exist. For example for two equal spherical bodies the center of gravity of the system is forced by symmetry, and lies midway between the centers; but gravity due to the system is not very large near that point.
Centres of gravity of simple objects
If two bodies are rigidly fixed to each other, then the center of gravity of the combination lies on the line joining the centers of gravity of the individual bodies.
In symmetric bodies, the CG lies on the line of symmetry. If there are two or more lines of symmetry, then the CG is at the point of intersection of these lines. The CG of a rectangle is at the intersection of the two diagonals. This principle is used in the example given below [Locating the center of gravity (2)]
Image:CoG_stable.jpg thumb|100px|Fig 1
The CG of a triangle lies on the
median (geometry) median (line joining the vertex to the mid-point of the opposite side). Hence, the CG of a trangle is the point of intersection of the medians.
It is not to be assumed that the CG of an object will always be ''on'' the object. For example, the CG of a ring will be at the center of the ring (in the air).
When the CG of an object is directly under or over the base (or support), the object is said to be in a state of stable equilibrium. It is possible to construct an object whose CG is always tends to come below the point used as the support such that the object will never topple. Many educational toys rely on this fact. Fig 1 is such an example. C is the CG of the toy and P is the point where it is supported.
Locating center of gravity (1)
{| border="2" cellspacing="2" cellpadding="2"
|-
| style="width:32%" |
Image:Center_gravity_0.png center
| style="width:32%" |
Image:Center_gravity_1.png center
| style="width:32%" |
Image:Center_gravity_2.png center
|-
| '''Step 1:''' Cut an arbitrary 2D shape.
| '''Step 2:''' Suspend the shape from a location near an edge. Drop a
plumb line and mark on the object.
| '''Step 3:''' Suspend the shape from another location not too close to the first. Drop a plumb line again and mark. The intersection of the two lines is the center of gravity.
|}
Locating center of gravity (2)
Here is an interesting way of determining the CG of an 'L' shaped 2-D object as given in fig 1:
Image:CoG of L shape.jpg 800px|CG of L shaped object
1) Divide the shape into two rectangles, as shown in fig 2. Find the CGs of these two rectangles by drawing the diagonals. Draw a line joining the CGs. The CG of the 'L' shape must lie on this line AB.
2) Divide the shape into two other rectangles, as shown in fig 3. Find the CGs of these two rectangles by drawing the diagonals. Draw a line joining the CGs. The CG of the 'L' shape must lie on this line CD.
3) As the CG of the shape must lie along AB and also along CD, it is obvious that it is at the intersection of these two lines, at O. The point 'O' may ''not'' lie inside the L-shaped object.
Differences between center of mass and center of inertia
There is no factual difference.
Center of mass, center of gravity or center of inertia are different names for the same thing.
References
*{{cite book | author=Serway, Raymond A.; Jewett, John W. | title=Physics for Scientists and Engineers (6th ed.) | publisher=Brooks/Cole | year=2004 | id=ISBN 0534408427}}
*{{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.) | publisher=W. H. Freeman | year=2004 | id=ISBN 0716708094}}
See also
* The
barycenter is the center of mass of two objects.
*
Center of mass
*
centroid
Category:Gravity
de:Schwerpunkt
es:Centro de gravedad
ja:�心
pl:Środek ciężkości
pt:Centro de gravidade
sl:TežiÅ¡Ä?e
tr:Ağırlık merkezi
see :
Center of gravity
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