Types of equilibrium of the rigid body

Not all things we find in everyday life always rest. Maybe at first the object rest, but if it is moved (for example by the wind) objects can move. The problem is, whether after moving, objects return to their original position or not. This depends on the type of balance of the object. After moving, there will be three possibilities, namely:

(1) the object returns to its original position,

(2) the object moves away from its original position,

(3) the object remains in its new position.

If after moving the object back to its original position, the object is in a stable balance. If after moving the object moves even further, then the object is in an unstable balance. Conversely, if after moving, the object remains in its new position, then the object is in a neutral balance.

1. Stable equilibria

An object that is initially rest, if on it exerted force or torque (there is a resultant force or resultant moment of force) then the object will move. Equilibrium is stable if after moving, the object returns to its original position. Moving objects return to their original position due to the resultant force or resultant moment of force that appears after the object moves.

Types of equilibrium of the rigid body 1Example 1. An object is hung by a rope on a buffer. First, the object is rest. After being pushed, the object moves and the object returns to its original position. The object’s weight is in the center of the object, while the support point is between the rope and the support. Moving objects return to their original position due to the resultant gravity in the horizontal direction (wx). The rope tension (T) and the gravity component in the vertical direction (wy) eliminate each other because these two forces have the same size but the opposite direction.

Types of equilibrium of the rigid body 2Example 2. The object in the valley. Initially object rest. After being moved, the object moves to the right and left, then returns to its original position. The ball moves return to its original position due to the resultant gravity in the horizontal direction (wx). The gravity component in the vertical direction (wy) and the normal force (N) eliminate each other because the two forces have the same magnitude but the direction is opposite.

Types of equilibrium of the rigid body 3Example 3. Initially object rest. The center of gravity is the center of the object and the point of support is at the base of the object in contact with the flat plane. After moving to the right, the object rises to the right. If the position of the center of gravity is still to the left of the fulcrum, then the object can still return to its original position. The object can move back to its original position due to the resultant moment of force generated by gravity. In this case, the support point acts as the axis of rotation. Conversely, if the object is moved to the left then the object lifted to the left. If the position of the center of gravity is still to the right of the support point, the object can still return to its original position.

Types of equilibrium of the rigid body 4For cases like example 3, objects are still in the stable equilibria if after being lifted, the center of gravity of the object does not pass through the support point. If after being lifted to the right, the center of gravity goes past the point of support, the object moves away from its original position. This is an example of unstable equilibria.

2. Unstable equilibria

Equilibria is unstable if the object is initially motionless due to the resultant force or the resultant moment of force acting on the object. After moving, the object does not return to its original position but away from its original position.

Types of equilibrium of the rigid body 5Example 1. An object that is initially motionless due to interference. After moving, the object keeps moving away from its position. Object away from its original position because after moving, the position of the center of gravity is to the right of the support point. When the center of gravity is to the right of the support point, the resultant moment of force arises which turns the object away from its original position.

Example 2. The object is at first above the peak.

Types of equilibrium of the rigid body 6After being moved, the object keeps moving away

from its original position. The object moves away from its position originally due to the presence of gravity components in the horizontal direction (wx).

3. Neutral equilibria

Neutral equilibria if after moving due to interference, the object stays in its new position. Objects do not move back to their original position and objects do not move away from the original position.

Types of equilibrium of the rigid body 7Example 1: A ball initially rest on a flat plane is moving. After stop moving, the ball stays in its new position. The ball doesn’t move back to its original position or not move away from its original position.

Based on the explanation above, it can be concluded:

First, if the center of gravity of the object is below the support point, the object is at stable equilibria. For example, an object is hung by a rope on a buffer.

Second, if the center of gravity of an object is above the support point, the equilibria of the object are relative. Objects can be stable, objects can also be unstable.

Types of equilibrium of the rigid body 8Third, the equilibrium of objects depends on the shape and size of objects. Wider objects are more stable than not wide objects.

Fourth, the equilibrium of objects depends on the distance of the center of gravity from the support point.

If the center of gravity is far from the support point, then the object is at an unstable equilibrium. Conversely, if the center of gravity is close to the support point, then the equilibrium is unstable.

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