A Short Note On Reynolds Number Significance

Partial equilibrium is a subpart of rigid bodies and their equilibrium. Rigid bodies are many particles grouped acting as a single unit or system. A rigid body is much like a regular particle and behaves or it can also be described as a body whose particles are always at a constant distance from one another and have little to no deformities in their structure. These bodies have different behavioral tendencies according to the type of motion that is applied to these rigid bodies. 

Irrespective of the force applied to a body the rigid bodies always maintain a constant ratio in the distance between the particles. Sometimes the rigid body experiences a phenomenon called “equilibrium”, where the net force applied to the rigid body becomes zero.

The textbook definition of equilibrium is when the object does not experience any form of energy or force be it negative or positive. In physics when the whole system comes to a balance in either internal or kinetic energy of the object/particle, the particle will continue to stay in this equilibrium state till there is an increase in any one opposing force resulting in the unbalanced force.

EQUILIBRIUM IN RIGID BODIES 

PREREQUISITE FOR RIGID BODY EQUILIBRIUM

Force

The motion of a body is caused due to the application of force. The application of force deforms, moves, and changes an object. It can allow us to change the position of a body, make it go faster or make it go slower, change the height of the body from the ground, etc. There are various types of forces that can act on a body ranging from frictional force to gravitational force.

Forces can be classified into two types: contact and non-contact forces. Forces that can be exerted only when the applicant of the force and the body on which it is going to be applied are in contact are called contact forces. Whereas forces that do not require the applicant of the force and the body on which it is going to be applied to be in contact are called non-contact forces.

Acceleration on a body

When force is applied to a rigid body already in motion with a fixed velocity v, then the application of the external force results in a change in the velocity of the body. The measure of the change in velocity to the time of a rigid body in motion due to the application of an external force is called acceleration. Let v be the velocity of a rigid body, then the acceleration of the body is given as a = dv/dt.

Inertia

According to Newton’s second law, all bodies tend to resist a change in their state. If a body is at rest it will resist a change to a state of motion and if a body is in motion then it will resist a change to a state of rest. But the property that measures this tendency of a body to resist a change in its state is called Inertia. Inertia is a measure of the amount of force that will be required to either stop a moving body and bring it to rest in unit distance or to put a body at rest into motion. Inertia is by the mass of the body and is an innate property of every object that has a mass.

Torque 

Torque is the force that causes an object to rotate about its access. It causes angular acceleration in other words it can be described as the rotational force equal in terms to linear force. Torque is a measure of the rotational force. The SI unit of torque is Nm. There are 2 types of torque: static and frictional. Its formula is: 

  = f • r (sinx)

The difference between particles and rigid bodies, rigid bodies ALWAYS have the potential to rotate around a point /axis whereas particles don’t have any potential torque.

Rigid bodies can experience both rotational and translational motion, hence equilibrium of rigid bodies we need to consider both the motions. The translational force in a rigid body is responsible for the change in momentum linearly whereas rotational motion is responsible for the change in momentum of the rigid body. Keeping these 2 forces in mind we get 2 types of equilibrium in rigid bodies.

CONDITIONS FOR RIGID BODY EQUILIBRIUM 

• The forces on rigid bodies are not concurrent, they may result in rotational motion 
• Net force and net momentum at any point (arbitrary) on the rigid body MUST be = 0
• Therefore there to be equilibrium in a rigid body we must have :

 Net Linear force = F = f1 + f2 … + fn = 0 and net angular force = 1+ 2 … + n = 0

TYPES OF RIGID BODY EQUILIBRIUM 

MECHANICAL EQUILIBRIUM 

In mechanical equilibrium, both linear momentum as well as angular momentum remain constant or do not show a change in a given period or there is no linear acceleration or angular acceleration. 

PARTIAL EQUILIBRIUM 

In partial equilibrium there is only translational equilibrium or linear motion is constant and there is no rotational equilibrium or the angular momentum is not constant or vice versa.  

In ‘partial’ equilibrium we have only one kind of equilibrium unlike mechanical equilibrium, for example, we can look at the diagram below:

This rod is attached in the middle, this has translational equilibrium as there is an equal force acting on both ends of this rod.

This results in the net translational force acting on the object being equivalent to 0.

CONCLUSION 

Equilibrium plays a vital role in our lives, even if we don’t see it there is equilibrium in small things such as a wall-mounted shelf if there would be a slight imbalance in the shelf’s forces it will fall. Rigid bodies are what we work in our everyday life hence understanding their working is beneficial to everyone and the concept of equilibrium and partial equilibrium makes us understand the concept in a crystal clear manner.