The centre of mass or mass centre is the mean location of all the mass in a system. In the case of a rigid body, the position of the centre of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space, such as shot from a shotgun or the planets of the solar system, the position of the centre of mass is a point in space among them that may not correspond to the position of any individual mass.
The term centre of mass is often used interchangeably with centre of gravity, but they are physically different concepts. They happen to coincide in a uniform gravitational field, but where gravity is not uniform, centre of gravity refers to the mean location of the gravitational force acting on a body.
The centre of mass of a body does not generally coincide with its geometric centre, and this property can be exploited. Engineers try to design a sports car‘s centre of mass as low as possible to make the car handle better. When high jumpers perform a “Finsbury Flop“, they bend their body in such a way that it is possible for the jumper to clear the bar while his or her centre of mass does not.
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If an object has uniform density then its centre of mass is the same as the centroid of its shape.
Examples:
The Centre of Mass of an arbitrary 2D physical shape can be found using the following plumbline method as illustrated in the following table:
Step 1: 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 centre of mass. |
This method is useful when one wishes to find the centroid of a complex planar shape with unknown dimensions. It relies on finding the centre of mass of a thin body of homogenous density having the same shape as the complex planar shape.
This is a method of determining the centre of mass of an L-shaped object.
1. Divide the shape into two rectangles, as shown in fig 2. Find the centre of masses of these two rectangles by drawing the diagonals. Draw a line joining the centres of mass. The centre of mass of the shape must lie on this line AB.
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