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Rabia
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Statics 

   Static is the branch of mechanics which deals with the study of bodies at rest under a number of forces, the equilibrium, conditions of equilibrium, types of equilibrium, torque etc.


Equilibrium

   A body is said to be in equilibrium if it is at rest or moving with uniform velocity.

   In other words,

if the linear and angular acceleration of a body are zero, the body is said to be in equilibrium.

   Or we can say that,

when two or more forces act on a body such that their resultant or combining effect on the body is zero and the body retains its state of rest or of uniform motion then the body is said to be in equilibrium


Example

book lies on the table, suspended bodies, all stationary bodies , jump by using parachute.


Types of equilibrium

   With respect to the state of a body, equilibrium may be divided into two categories:

   1. Static equilibrium.

   2. Dynamic equilibrium.


    Static equilibrium

   If the combined effect of all the forces acting on a body is zero and the body is in the state of rest then its equilibrium is termed as static equilibrium.

   For example: All stationary bodies


Dynamic equilibrium

   when a body is in state of uniform motion and the resultant of all forces acting upon it is zero then it is said to be in dynamic equilibrium.

   For example: Jump by using parachute.


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September 14, 2009 at 2:28 PM Flag Quote & Reply

Rabia
Site Owner
Posts: 1094

 

States of equilibrium

   There are three states of equilibrium:    

  • Stable equilibrium
  • Unstable equilibrium
  • Neutral equilibrium


Stable equilibrium

   When the center of gravity of a body lies below point of suspension or support, the body is said to be in STABLE EQUILIBRIUM.


For example a book lying on a table is in stable equilibrium.


Explanation

   A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge and then allowed to fall, it will come back to its original position.

   Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.


Reason of stability

   When the book is lifted its center of gravity is raised . The line of action of weight passes through the base of the book. A torque due to weight of the book brings it back to the original position. 




Unstable equilibrium

   When the center of gravity of a body lies above the point of suspension or support, the body is said to be in unstable equilibrium


Example

   pencil standing on its point or a stick in vertically standing position.



Explanation:

   If thin rod standing vertically is slightly disturbed from its position it will not come back to its original position. This type of equilibrium is called unstable equilibrium,

other example of unstable equilibrium are vertically standing cylinder and funnel etc.


Reason of instability

   when the rod is slightly disturbed its center of gravity is lowered . The line of action of its weight lies outside the base of rod. The torque due to weight of the rod toppled it down.




Neutral equilibrium

   When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium.


Example: rolling ball.


Explanation

   If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. This type of equilibrium is called NEUTRAL EQUILIBRIUM.


Reason of neutral equilibrium

   If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity is at the same height as before.



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September 14, 2009 at 2:29 PM Flag Quote & Reply

Rabia
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Posts: 1094

CENTRE OF MASS   .


DEFINITION 

The centre of mass of a body or a system of particles is defined as

"A single point at which the whole mass of the body or system is

imagined to be concentrated and all the applied forces acts at that point."


  

EXPLANATION

In translational motion each point on a body undergoes the same displacement as any other point as time passes, so that motion of one particle represents the motion of the whole body. But when a body rotates or vibrates, there is one point on the body, called "centre of mass", that moves in the same way that a single particle would move under the influence of the same external forces.

   Centre of mass of a body is that point that moves when forces are applied on the body. The motion of a body can be described as the motion of its centre of mass.

   The centre of mass , has translational motion under the influence of forces. If a single force acts on a body and the line of action of the force passes through the centre of mass, the body will have linear    acceleration but possess no angular acceleration.


CENTRE OF MASS & CENTRE OF GRAVITY   

The centre of mass often confused with the centre of gravity. The two terms are so similar in many respects that one can use the two interchangeably. The centre of gravity of an extended object coincides with its centre of mass if the object is in a completely uniform gravitational field. If the body is not located in a uniform gravitational field,its centre of mass and centre of gravity will be at two different locations.




CENTRE OF MASS OF DIFFERENT OBJECTS

   Centre of mass of a body depends on its geometrical shape. If a body is symmetrical and of uniform composition, the centre of mass will be located at its geometrical centre.


 For example:

Centre of mass of a square is at the point of intersection of its diagonals.

Centre of mass of a sphere is at its centre.

Centre of mass of a rigid bar is at the middle point.



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September 14, 2009 at 2:51 PM Flag Quote & Reply

Rabia
Site Owner
Posts: 1094

LAW OF CONSERVATION OF ANGULAR MOMENTUM

.

IT STATES THAT:

"When the net external torque acting on a system about a given axis is

zero , the total angular momentum of the system about that axis remains constant."    


Mathematically, If  then   = constant   


Proof

   According to the second law of motion net force acting on a body is equal to its rate of change of linear momentum.

   i.e.






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September 14, 2009 at 3:05 PM Flag Quote & Reply

Rabia
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Posts: 1094



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September 15, 2009 at 4:06 AM Flag Quote & Reply

Rabia
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Posts: 1094



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September 15, 2009 at 7:48 AM Flag Quote & Reply

Rabia
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Posts: 1094



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September 15, 2009 at 7:51 AM Flag Quote & Reply

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