Displacement Mechanics

A study generally performed on the displacement of the object is the displacement mechanics. 

We all like to take a shortcut in our lives or while driving to our office while getting late, so the shortest path we take is displacement.

A displacement is a vector form of the shortest distance between the initial position and the final position.

On this page, also we will discuss what is displacement, displacement definition, displacement meaning in Physics, displacement of the particle, be it having a linear motion or the circular motion.

What Is Displacement?

If you are curious to know what displacement is, look at the following diagram:

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Let’s suppose that the distance between points A and B is 30 m and the shortest path between these points is along the way, which is just 16 m from your destination. If you are asked which path you will choose?

Definitely, you will travel through the 16 m path line, so this path line is the displacement (this is the displacement definition).

Displacement Definition Physics

Now, let us understand the displacement definition with the help of a known term ‘distance’:

Example 1:

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Soham walks from point A to B to C. What distance, does he travel? What is the displacement?

Let's first calculate the distance Soham travels. While calculating distance, we look at the numerical value of the distance interval between the travelled points. As we can see from the above figure that he travels from A to B, then B to C. Distance from point A to B is 4m and from B to C is 3 m. So, their sum will give us total distance as;

4 m + 3 m = 7 m

Now, it's time to calculate displacement. Since displacement is a vector quantity, so it has both magnitude and direction. 

In our stated example, the initial point is A and the final point is C. Displacement vector is an interval between the initial and final points. As it can be clearly seen that the interval between A to C is 5m. So, our displacement vector is 5m and its direction is from point A to C.

Let’s look at another example:

Example 2:

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We find distance taken by an object as;

From A to B =10 - 2 = 8m

From B to C = 10 - 2 = 8m

Then, from C to D = 10 - 6 = 4m

Total distance traveled from point A to point D is;

=>    8m + 8m + 4m = 20m

Now, we can find the final displacement by drawing a straight line from point A to the final point F. As we can see from the above graph, the object changes its position to 8m. So, the displacement is given as;

Displacement = Final position - Initial position

Displacement = 10m - 2m = 8m

Displacement Mechanics

Now, let us understand the displacement mechanics with the help of the below diagram:

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Look at the image above, you can see there are two multiple paths between point P’ and P. Now, the distance that lies very close to both is indicated by the path line. This path line is nothing but displacement. 

Since displacement is indicated by a direction with the magnitude, we call this quantity a vector. A displacement vector is represented by an arrow-head, where an arrow indicates the direction and the tail follows it.

Here, we considered a field of displacement to represent the displacement mechanics, now let’s understand the displacement field.

Mechanical Displacement

A displacement field is assigning the displacement vectors for all points in a region for a body that is displaced from one position to another. 

A displacement vector specifies the position of the displacement of a particle in reference to an origin or to a previous position. 

For example, a displacement field may be used to describe the effects of deformation on a solid body that we study in the concept of stress and strain.

Before discussing displacement, the position before deformation must be defined. It is a state in which the coordinates of all points are known and described by the following function:

P_o^➝: Ω ->Q ….(1)

Where

Po^➝ is a displacement vector

are all the points of the body

Q are all the points in the space in which the body resides

Force Into Displacement

In the above equation (1), we understand that the displacement vectors point to all the directions of an object.

Most often it is a state of the body in which no force to displacement is applied, then given any other state of this body in which coordinates of all its points are described in the following manner:

v^➝ = P₁^➝ - P_o^➝…..(2)

From the above equation (2), we can see that the displacement field is the difference between two body states or positions.

and, v^➝ is a displacement field, which for each point of the body specifies a displacement vector.