Equations for Circular Motion
Acceleration which an object faces in circular motion generally has two components:-
- Tangential Acceleration (aT)
- Radial Acceleration (aR)
When the object moves in a circular path, it experiences two different acceleration which works for two different purposes. One acceleration provides the magnitude of acceleration to the object while the other one is responsible for its direction. The acceleration which is responsible for the magnitude is called as tangential acceleration or linear acceleration. The acceleration which is responsible for the direction of the object moving in a circular path is called radial acceleration or centripetal acceleration. Both the tangential and the centripetal acceleration are perpendicular to each other.
Centripetal acceleration acts towards the centre of the circle and keeps the object in a circular path. This centripetal acceleration is further responsible for the Centripetal force. The normal reaction of this force is Centrifugal force which is equal in magnitude and opposite in direction to the centripetal force.
As we know the centripetal acceleration is given as, ac = V2/R. Since this acceleration is responsible for the centripetal force , therefore the centripetal force is given by,
F = mac = mV2/R
We also know from above that ω = V/R
Putting the value of V from above in centripetal force, we get,
F = mRω2
Since the object is moving in a circular path, the object must have taken some time to complete one full revolution. As we know that the time taken by the object to complete one full revolution is defined as its time period. It is denoted by T. A similar but slight different concept is frequency, which is the number of revolution made by the object in one second. Frequency is denoted by ν.
ν = 1/T
In a complete revolution, the object will move a distance of S = 2πR. Therefore, we will have V = 2πR/T
In terms of frequency we can write V = 2πRν. The angular velocity can be written as, ω=2πν. The centripetal acceleration can be written as, ac = 4π2ν2R
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