Angular Displacement Formula

Angular Displacement Formula

The notion of Angular Displacement informs students about the concept of displacement, which will be covered later. It is especially relevant to the Physics discipline. Extramark has provided students with material on this topic to help them comprehend it better. The website also provides numerous more study materials for pupils to practise, learn, and improve their level of preparedness. Extramark’s website provides revision notes, textbooks from various boards and institutions, worksheets, sample papers, previous year’s question papers, and other tools to help students prepare for exams.

Angular Displacement Formula

Rotational Motion refers to the motion of the body in a circular route. The displacement caused by such motion differs from that caused by linear motion; it is frequently in the shape of an angle, thus the name Angular Displacement. Below, we will examine Angular Displacement and the formula; let us describe it using examples.

Angular Displacement refers to the angle created by the body when travelling in a circular direction. Before we can get into more detail, we must first define rotational motion. When a rigid body rotates along its axis, the motion no longer becomes a पार्टिकल।

Because of the motion along the circular route, acceleration and velocity might vary at any time. Rotational motion is defined as the motion of rigid things that stay constant during the rotation around a given axis.

Angular Displacement Definition

To define Angular Displacement, assume a body is moving in a circular motion. The angle created by a body from its point of rest at any point in rotational motion is referred to as angular displacement.The shortest angle between an object’s beginning and final positions in a circular motion around a fixed point is known as Angular Displacement, and it is a vector variable.

Unit of Angular Displacement

Radian, often known as degrees, is the unit of angular displacement. 360 degrees is equivalent to two pi radians. Metre is the SI unit of displacement. Because angular displacement requires curvilinear motion, the SI unit is degrees or radians.

Measurement of Angular Displacement

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

where,

θ is the angular displacement,

s is the distance travelled by the body, and

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

In simpler words, the displacement of an object is the distance travelled by it around the circumference of a circle divided by its radius.

Angular Displacement Derivation

Let’s take an object performing linear motion with initial velocity u and acceleration a. After time t the final velocity of the object is v and total displacement during this time is s then,

a = dv / dt

dv = a×dt

Integrating both sides, we get,

∫^v_udv = a×∫dt

v – u = at

Also,

a = dv / dt

a= (dv / dx) / (dx/ dt)

As we know v = dx/dt,

a = v (dv / dx)

v dv = a dx

After integrating both sides of the equation,

∫^v_u vdv = a∫dx

v² – u² = 2as

Now, substituting the value of u from v = u + at

v² − (v − at)² = 2as

2vat – a²t² = 2as

s = vt – 1/2at²

Finally replacing  v with u we get,

s = ut + 1/2at²

Solved Examples

Example 1: Risabh travels around a 50 m diameter circular track. What is his angular displacement if she runs around the entire track for 150 m?

Solution:

Given,

• s = 150 m
• d = 50 m
• r = 25 m

We have, θ = s / r

θ = 150/25

θ = 6 radians

Example 2: Raj purchased a pizza with a radius of 0.4 meters. A fly lands on the pizza and wanders 120 cm around the edge. Calculate the fly’s angular displacement.

Solution:

Given,

• r = 0.4 m
• s = 120 cm = 0.12 m

We have, θ = s / r

θ = 0.3 rad