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Home / Physics / Angular Motion: Definition, Relationship with Linear Motion, and FAQs

Angular Motion: Definition, Relationship with Linear Motion, and FAQs

Last Updated on Feb 20, 2025
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In the realm of physics, we often deal with equations and formulas that calculate linear velocity and displacement. But did you know there are also corresponding formulas for angular movement? It's like having a twin for each of the linear motion equations. In this comprehensive guide, we'll delve into the fascinating world of angular motion and explore its connection with linear motion.

Table of Contents

Defining Angular Motion

So, what exactly is angular motion? Let's break it down:

Angular motion refers to the movement of a body around a fixed point or axis. It's the angle traversed by a line drawn to the body from the point or axis.

The Connection between Linear and Angular Motion

To understand the relationship between linear and angular motion, let's look at a few variable substitutions that can help us derive the formulas for angular motion:

  • Displacement – In linear motion, we use the symbol ‘ s ’ to represent the linear distance covered. However, in angular motion, we use ‘ θ ’ to represent the angular distance, which is measured in radians.
  • Velocity – In linear motion, the symbol ‘ v ’ is used to denote velocity. In contrast, in angular motion, we use the symbol ‘ ω ’ to represent angular velocity, defined as the number of radians covered per second.
  • Acceleration – The symbol ‘ a ’ is used to denote linear acceleration, while the symbol ‘ α ’ represents angular acceleration . Angular acceleration is measured in radians per second 2 .

Now that we understand the differences and similarities between linear and angular motion, let's examine the corresponding formulas for both types of motion.

Formula

Linear

Angular

Velocity

Acceleration

Displacement

Motion with time cancelled out

To better understand the relationship between linear and angular velocity, let's consider a new example. Imagine a spinning top. It completes one full rotation, equivalent to 2π radians, in just 1 second. Using the formula for angular velocity, we can calculate the top's average angular velocity as follows:

This example illustrates the convenience of using radians to measure angles. It also allows us to easily relate the linear speed to the angular speed.

We can relate the linear speed to the angular speed using the following steps:

Starting with the equation,

We multiply both sides of the equation by the radius r ,

Now, the term rΔθ represents the distance travelled by an object moving in a circle with radius r . So the equation becomes

Recognizing the right side of the equation as the formula for speed, we can write the relationship between linear and angular speed as:

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Frequently Asked Questions

The relationship between linear and angular speed is given by the formula: rω = v

Angular velocity is defined as the number of radians covered per second.

SI unit of the angular acceleration = Rad/s^2.

The formula for acceleration in angular motion is a=Δω/Δt

The formula to calculate displacement in angular motion is Θ =v_i*t+1/2*α*t^2

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