Basics of Circular Motion
What makes something move in a circular path?
When an object is in circular motion its path is confined to a circle of fixed radius. Let us try to understand the basic laws that govern the motion of such an object.
Consider an object moving in a circular path of radius (R), initially at pint P and reaches point Q in time (t), as shown in the image below
The distance covered by the object during the course of circular motion is measured in terms of the angle that it makes about the center of the circular path from its initial position. This displacement is called Angular displacement.
In the above image the angular displacement is:
It is simply the speed with which the body moves in the circular path. More systematically, it is the ratio of angular displacement to the time taken by it to cover the distance.
Time period and Frequency
Time period is the time taken by the body in circular motion to complete one revolution. It is denoted by (T). In a complete revolution it covers 2π radians. Thus the angular velocity is
Frequency is the number of revolutions per second. It is denoted by ν (Greek letter Nu)
From the above equations we can say that
Kinematical equations of circular motion
The basic equations of motion can be rewritten as follows
Where α is the angular acceleration
Uniform circular motion
When a body moves in a circular path of fixed radius at a constant speed, then the motion of that object is called a uniform circular motion.
During a uniform circular motion, the direction of the velocity vector changes continuously. But according to Newton’s laws of motion there must be an external force to change the direction of motion.
This force plays the role of that external force responsible for the change of direction of motion in a uniform circular motion.
As a result of this force there is an acceleration called centripetal acceleration directed towards the center of the circular path
The centripetal force is given by
Further it can be written as
Real life example:
Consider a merry go round with a mass of 50 kg kept on the blue position and revolving in an anticlockwise direction with velocity v. Then the force experienced by the mass is given by
The outward force experienced by an object in circular motion is called centrifugal force.
Note: Centrifugal force is not a real force
It is given by
It can be studied in terms of inertia but still inertia is not the actual cause of it. Below is an animation of a body in uniform circular motion.