Related Concepts to Circular Motion
There are various new terms which comes into the picture when we talk about circular motion. These new terms generally arises from the fact that in circular motion there is angle involved so the terms, such as, angular displacement, angular velocity, or angular acceleration. The image added below shows the Angular Velocity and others in an object performing circular motion.
Let’s see these concepts one by one.
Angular Displacement
Angular displacement can be defined as the measurement of the amount of rotation an object has gone through in a circular path. In circular motion, the object moves in a circular path, and angular displacement helps us observe the position of the object in a circular path. It can also be understood as the angle made by the position vector of the object between its final and initial position in the circular path.
Angular displacement is a vector quantity. The SI unit of the angular displacement is radians. It is conventionally denoted as θ. The mathematical representation of angular displacement is,
Angular Displacement(θ) = Arc Length/Radius
Therefore,
θ = S/R
where,
- S is Linear Displacement Done by Object on Circular Path
- R is Distance of Object from a Fixed Central Point (Called Radius)
Angular Velocity
Angular velocity can be defined as the rate of change of angular displacement. It is analogous to the linear velocity as it is the rate of change of linear displacement. Angular velocity can also be understood as the rate at which an object moves in a circular path.
- Angular velocity is a vector quantity. It is denoted by ω.
- SI unit of angular velocity is radian per second (rad s-1).
Mathematically, angular velocity can be represented as,
Angular Velocity (ω) = dθ/dt
We know from above that, θ = S/R
Using Angular Displacement in above equation,
ω = d/dt.(S/R)
which gives,
ω = 1/R.(dS/dt)
Finally,
ω = v/R
where,
- V is Linear Velocity and V = dS/dt
- R is Distance of Object from a Fixed Central Point
Angular Acceleration
Angular acceleration can be defined as the rate of change of angular velocity. It can be understood as the measurement of how fast or slow the angular velocity of an object is changing on the circular path. When any object starts from rest and acquires motion in circular path, it is said to have angular acceleration working on it. For example, when the Ferris wheel starts from the rest and acquires the speed, then the pods of the Ferris wheel gains angular acceleration. When the angular velocity increases, then the angular acceleration is positive. But when the angular velocity decreases, the angular acceleration is negative, i.e., angular deceleration.
- Angular acceleration is vector quantity. It is denoted by α.
- SI unit of angular acceleration is radian per second squared (rad s-2).
Angular acceleration can be represented as,
Angular acceleration (α) = dω/dt
We can substitute ω = v/R in above equation to get,
α = d/dt (v/R)
α = 1/R (dv/dt) = 1/R.(a)
Since, rate of change of linear velocity is called linear acceleration, therefore, above equation can be written as,
α = a/R
where,
- a is Linear Acceleration of Object
- R is Distance of Object from a Fixed Central Point
Circular Motion
Circular Motion is defined as the movement of an object rotating along a circular path. Objects in a circular motion can be performing either uniform or non-uniform circular motion. Motion of a car on a bank road, the motion of a bike well of death, etc. are examples of circular motion.
In this article, we will learn about circular motion and some related concepts, such as examples, equations, applications, etc.
Table of Content
- What is Circular Motion?
- Equations for Circular Motion
- Centripetal Force
- Centrifugal Force
- Types of Circular Motion
- Circular Motion and Rotational Motion
- Circular Motion Formulas