Rotational Equilibrium:
When an object is in equilibrium, it is not moving or rotating. The object's linear and angular accelerations are both zero.

* The sum of all the torques acting on a system must be equal to zero.

* The sum of the clockwise torques must be equal to the sum of the counterclockwise torques.

* The pivotal axis can be chosen to be any point inside or outside the object.

* It useful to observe that choosing the pivot point through the line of action of a force eliminates that force from the equilibrium torque equations. This often simplifies things.


Linear Static Equilibrium of the Center of Mass:
* The vector sum of all the forces acting on the object must be equal to zero.

* The sum of the horizontal components of all the forces must be equal to zero, and the sum of the vertical components of all the forces must be equal to zero.

* The sum of the components of the forces to the right must be equal to the sum of the components of the forces to the left, and the sum of the components of the forces up must be equal to the sum of the components of the forces down.


Torque Due to the Weight of an Object:
* The torque on a solid body (about any axis) produced by the object's own weight can be calculated as if all the object's mass were located at the center of mass of the object. Here the lever arm is the distance between the pivot point and the center of mass.

* Since freely rotating systems revolve about their center of mass, the weight of an object cannot create any torque on the object when it is rotating freely.


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