# Linear Displacement And Angular Displacement: 9 Facts

Understanding kinematics begins with learning basic concepts in motion. Let us discuss on linear displacement and angular displacement.

Linear displacement is the distance between the initial and final positions of motion of a body moving in a straight line. Angular displacement which occurs in curvilinear motion is the difference between the initial and final positions of the object, measured in angles.

## What is linear displacement?

Robots and machine tools involve motion in a linear fashion. Let us see what linear displacement all about is.

Linear displacement is the displacement of an object during its motion in a straight line. Its magnitude is given by the distance (in units of length) between the object’s initial and final positions, while direction is denoted by either positive or negative sign as it involves only two directions.

## What is angular displacement?

It is not necessary that an object always follows a linear path. Let us discuss about angular displacement when the object is in curvilinear motion.

Angular displacement is the measure of the angle (in degrees or radians) subtended when an object moves from one location to another along a circular path. Being a vector quantity, direction of angular displacement is determined by the right hand thumb rule.

To be more precise, if the initial position of a particle is at an angle θ1 and the final position is at another θ2 with respect to a reference line, then angular displacement is given by the difference between the two angles, θ = θ2 – θ1.

## How is linear displacement related to angular displacement?

Angular displacement can be regarded as an angular analogy to linear displacement. Here, we shall look upon the relationship between the two quantities.

• Angular displacement is directly proportional to linear displacement.
• The formula explaining the relation is θ = s/r. Here, θ is the angular displacement in radians or degrees (2π radians is equal to 360 degrees), r is radius in units of length, s is the linear distance or displacement in units of length.

## Difference between angular and linear motion

Well, a car moving on a straight road and a ball tied to a string whirling around portray different motions. Let us differentiate between linear and angular motion.

Motion of a cyclist along a straight road, motion of a boy running on a linear track are examples for linear motion. Motion of the fan blades, motion of children in merry-go-round are examples of angular motion. Parameters such as displacement, velocity in linear motion are termed angular displacement, angular velocity in angular motion.

## Difference between linear displacement and angular displacement

Displacement is a vector that is quantified by both magnitude and direction. Let us figure out how the term differs in linear motion and angular motion.

The direction of displacement in both motions are determined in a different manner. It is either up or down/side-to-side in linear displacement, hence positive or negative. In angular displacement, right hand thumb rule gives the direction. If the motion is anticlockwise, thumb points upwards and hence positive; otherwise vice versa.

## Can linear displacement and angular displacement be same?

Linear displacement and angular displacement are two physical quantities that we come across in kinematics. Let us examine if both the quantities can be the same.

Linear displacement and angular displacement cannot be the same, although it is misinterpreted as displacement. In physics, only those quantities with similar dimensions can be considered equivalent. Linear displacement has the dimensions of length while angular displacement has no dimensions.

## Linear Displacement And Angular Displacement: Numerical

The wheel of a two-wheeler (bicycle) has a diameter of 30 cm. It rotates about 10 radians. Find the linear displacement of a point on the wheel edge.

Solution:

Given, the diameter of a bicycle wheel = 30 cm

Therefore, radius of wheel = 30/2 cm = 15 cm

Angular displacement of the wheel = 10 radians

We have to determine linear displacement. The formula relating angular and linear displacement is

θ = s/r

10 = s/15

s = 10 × 15 cm

s = 150 cm

Hence, linear displacement of a point on the edge of the bicycle wheel is 150 cm.

#### Summary

Overall, a basic idea of linear displacement and angular displacement has been described with special emphasis given to linear and angular motions. In addition, the solved numerical demonstrates the use of formulas relating angular and linear displacement.

Deeksha Dinesh

Hello, I am Deeksha Dinesh, currently pursuing post-graduation in Physics with a specialization in the field of Astrophysics. I like to deliver concepts in a simpler way for the readers.