Saturday 10 September 2011

EQUILIBRIUM

DEFINITION: -
"The state of a body in which under the action of several forces acting together, there is no change in the translational motion as well as its rotational motion is called equilibrium".
Infect A body is in translational equilibrium if it is at rest, or is moving at constant speed in a straight line. It is in rotational equilibrium if it is rotating at constant angular speed about a fixed axis,
A body at rest and in equilibrium is said to be in a state of static equilibrium. A book lying on a table and a lamp hanging from a ceiling are best examples of static equilibrium. An air craft flying with constant velocity and a paratrooper falling down with constant terminal velocity are examples of dynamic equilibrium. A wheel, a disc or a grindstone rotating about its axis with constant angular speed are examples of dynamic rotational equilibrium.
So therefore we can say easily that from the definition of equilibrium there are two conditions that is AT REST  & UNIFORM MOTION so it is discussed below:
FIRST CONDITION OF EQUILIBRIUM: -
A body that remains at rest or moves with constant velocity is said to be in a state of equilibrium. In order that  a body be in equilibrium under the influence of any number of concurrent forces, the following condition must be satisfied.
DEFINITION: -
"The vector sum of all the forces acting on the body must be zero". If we draw a vector diagram to represent the forces, the above condition equivalent to the condition that the force polygon must close. In case of coplanar forces, we often resolve the forces into x and y components. In terms of x and y components, a body will be in translational equilibrium only if the algebraic sum of the x and y forces acting on the body is zero. Usually we choose the x and y aces as the horizontal and vertical axes. In this case we state the first condition of equilibrium as follows:
  • The sum of the rightward forces equals the sum of leftward forces:
  • The sum of the upward forces equals the sum of downward forces:
SECOND CONDITION OF EQUILIBRIUM: -
In many instances an extended body will not remains at rest even when the first condition of equilibrium is satisfied. But some additional restriction must be made on the rotational motion of the body if it is to be in equilibrium. We know that torque produces rotation in a body at rest or changes the angular velocity of a body. Thus the following condition, known as the second condition of equilibrium, must be satisfied to ensure rotational equilibrium.
DEFINITION: - 
"The vector sum of all the torques about any axis must be zero". This is equivalent to saying that the sum of all clockwise moments about any axis equals the sum of all anticlockwise moments about the same axis:
CLOCKWISE TORQUES = CLOCKWISE TORQUES
When the first condition is satisfied , it guarantees that there is no unbalanced force: no linear acceleration and the body is in transnational equilibrium. However, this condition does not ensure that there will be no change in rotatory motion. The second condition guarantees that there will be no net torque and no change in the rotational motion of a body under the influence of forces. The second condition is also necessary but not sufficient to ensure complete equilibrium.

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