[Physics Class Notes] on Angular Displacement Pdf for Exam

The concept of Angular Displacement teaches the students the concept of Displacement in the way it is discussed here later. It is specifically related to the Physics  subject. has provided the students with information on this topic to help them understand the same easily. The site also makes available many more study resources to let the students practice, learn, and enhance their level of preparation. The resources available on ’s website include revision notes, textbooks from various boards and institutes, worksheets, sample papers, previous year’s question papers, and others to facilitate improved exam preparation.

What Is Angular Displacement?

The motion of the body along a circular path is known as Rotational Motion. The Displacement done through such a type of motion is different from the Displacement done on linear motion; it is usually in the form of an angle, and hence it is known as Angular Displacement. Below we discuss Angular Displacement along with the formula, let us define it with the help of examples.

While moving in a circular path, the angle made by the body is known as Angular Displacement. Before discussing further on the topic, we have to understand what rotational motion is. The motion ceases to become a particle when a rigid body is rotating about its axis. Due to the motion in the circular path, change in the acceleration and velocity can happen at any time. Rotational motion is defined as the motion of the rigid bodies that will remain constant throughout the rotation over a fixed axis.

Angular Displacement Definition 

To define Angular Displacement, let’s suppose a body is moving in a circular motion, the angle made by a body from its point of rest at any point in rotational motion is known as Angular Displacement.The shortest angle between the initial and the final position for an object in a circular motion around a fixed point is known as the Angular Displacement; it is considered a Vector quantity.

 

Unit of Angular Displacement

The unit of Angular Displacement is Radian or Degrees. 360o is equal to two pi radians. Meter is the SI unit for Displacement. Since Angular Displacement involves the curvilinear motion, the SI unit for Angular Displacement is Degrees or Radian.

 

Angular Displacement Formula

The Formula of Angular Displacement

For a point the Angular Displacement is as follows:

Angular Displacement = θf-θi The Displacement will have both magnitudes as well as the direction. The circular arrow pointing from the initial position to the final position will indicate the direction. It can either be clockwise or anticlockwise in direction.

It can be measured by using a simple formula. The formula is:

θ=s/r, where,

θ is Angular Displacement,

s is the distance traveled by the body, and

r is the radius of the circle along which it is moving.

Simplistically, the distance traveled by an object around the circumference of a circle divided by its radius will be its Displacement.

 

Derivation

The Angular Displacement can be calculated by the below formula when the value of initial velocity, acceleration of the object, and time are shared.

[theta = wt + 1/2alpha t^{2}]

Where,

θ- Angular Displacement of the object

t- Time

α- Angular acceleration

Now, the formula for Angular Linear is

In Rotational, the kinetic equation is

[omega = omega 0 + alpha t]

[triangleomega = omega_{0}t+1/2alpha t^{2}],

[omega^{2} = omega_0^2 + 2alphatheta],

 

In translational, the kinetic equation is

v=u+at

or [s = ut+1/2at^{2}]

v2 = vo2 + 2ax

 

Where,

ω- Initial Angular velocity

 

Considering an object having a linear motion with initial acceleration a and velocity u, when time t and the final velocity of the object is with the total Displacement s then,  

a = dv​/dt

The change in velocity

 The rate which can be written as 

dv = a dt

Integrating both the sides, we get,

∫uv​dv=a∫0t​dt

v – u = at

Also,

a=dv/dt​

a=dxdv​/dtdx​

As we know v=dx/dt​, we can write,

a=vdv/dx​

v dv=a dx

The equation we get after integrating both sides

∫uv​vdv=a∫0s​dx

[V^{2}-u^{2} = 2as]

From the equation -1 into equation – 2 by substituting the value of u, we get

[V^{2}−(v−at)^{2}=2as]

[2vat–a^{2}t^{2}=2as]

By dividing the equation of both sides by 2a, we have

[s=vt–1/2at^{2}]

And at last, the value of v being substituted by u, we will get.

[s=ut+1/2​at^{2}]

 

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