Short Note on the Equilibrium of Rigid Bodies

Have you ever tried to balance the seesaws in the park? Or try to balance a book by your palm. All these phenomena in physics are examples of equilibrium. In a simple sense, where there is a balance between objects, they are said to attain equilibrium. In the equilibrium of rigid bodies, rigid bodies refer to those objects that do not change or convert over time. 

The equations of equilibrium of rigid bodies extend to two-dimensional as well as three-dimensional bodies. The two-dimensional bodies follow three equations of equilibrium of rigid bodies. In comparison, there are around six equations for the equilibrium of rigid bodies in 3d. However, understanding the concepts of equilibrium and rigid bodies is essential for understanding the equilibrium of rigid bodies. 

This article will discuss what equilibrium is in physics, what are rigid bodies, and the examples of the equilibrium of rigid bodies.

What Is Equilibrium in Physics?

In physics, equilibrium refers to the state of balance. It is said to be attained when there is no change between the state of motion and internal energy. That is, the object or the body’s motion and internal energy incline at a consistent level. An object attains equilibrium when it does not go through a shift. Once it goes through a change, there is an external party of force in work.  

Equilibrium can be understood with a common example. For instance,

A seesaw can be at a state of equilibrium. It is said to be at rest or in the state of equilibrium when both of its ends are equal. However, two children who ride on the seesaw will eventually debunk the state of its equilibrium. Here, the two children are said to be exerting the external force. Due to this, both ends of the seesaw would not only experience force but will also have a difference in the force exerted. 

For an object to attain equilibrium, it must comply with two conditions. These are:

• The net force of the object from all directions must be zero. That is, the force that is exerted on the object from different directions should not exceed zero. If it does, then the object is not in an equilibrium state. 
• Secondly, the net torque acting on the object must be zero. Here, torque refers to the rotational ability of the object. In the case of equilibrium, this torque should exert no force on the object. If there is any kind of accelerated rotation, the equilibrium position of the object becomes null. 

An object that is at a constant velocity is said to be in equilibrium. This is explained with the help of Newton’s second law. Constant velocity means zero velocity. So, the acceleration is constant too, which indicates that it is zero. Therefore, the external working force is also zero. This indicates that the force exerted from all directions is zero. Hence, the object with constant velocity is in equilibrium. 

Equilibrium of rigid bodies requires an understanding of what rigid bodies in physics are. The next section elaborates the same.

What Are Rigid Bodies in Physics?

Rigid bodies refer to those objects or bodies which remain unchanged. That is, whenever there is an external force applied at the two ends of these bodies, they remain unchanged in motion and internal energy. In other words, rigid bodies do not change shape when put under the pressure of external forces. 

In a rigid body, the distance between its two ends is constant and does not change. There is a continuous distribution of mass in rigid bodies. There are various examples of rigid bodies such as metal, tables, chairs, etc. Basically, anything that does not deform its shape due to the applied external force is said to be a rigid body.

Equilibrium in Rigid Bodies

Equilibrium of rigid bodies refers to the unchanged behaviour of these bodies when an external force is applied. There are two types of motions associated with  In terms of the equilibrium of rigid bodies – translational motion and rotational motion. Translational motion is said to be a motion in which the object shifts from one point to another. Rotational motion is said to be the motion wherein the object travels around a circular path. 

Translational motion keeps the bodies moving parallelly. That is, when two rigid objects travel in translational motion, they are parallel and constant to each other. Further, when the net force on a rigid body is zero, the body depicts translational equilibrium. This is because the linear momentum does change and remains constant. 

When the net force of the external torque is zero on the rigid body, it depicts a rotational equilibrium. Here, rotational equilibrium refers to the consistency of the rigid body in rotational motion. Further, there is also no kind of shift in the angular momentum. Angular momentum refers to the velocity at which the rigid bodies rotate. 

Examples of the equilibrium of a rigid body include the movement of the Ferris wheel, the movement of the seesaw, and many others.

Equations of Equilibrium of Rigid Bodies

There are derivations of the equations of equilibrium of rigid bodies. There is a common equation of equilibrium of rigid bodies in 3d and two-dimensional bodies. This equation is calculated as the sum of the force in the x and y directions with the moment of force in the z-axis. 

Symbolically, it is represented as:

Equilibrium of Rigid Bodies:

x+y+z = 0

Here, 

x= object 1 force

y= object 2 force

z= moment of force

Since the force in the directions of x and y has no impact on the objects, it is zero. Similarly, there is no shift in the moment of force, which indicates that the equilibrium of rigid bodies is 0.

Conclusion

This article discussed the equilibrium of rigid bodies in 3d and 2d. In physics, equilibrium refers to the state of balance. It is said to be attained when there is no change between the state of motion and internal energy. Further, examples and equations of equilibrium of a rigid body were covered.