Uniform motion in a circle

Understanding Uniform Circular Motion

Uniform Circular Motion refers to the movement of an object along the circumference of a circle at a constant speed.
Although speed is constant, velocity is continually changing due to, by definition, a changing direction.
The change in direction results in acceleration, even at constant speed.

The required acceleration for uniform circular motion is called centripetal acceleration.
Centripetal acceleration is always directed towards the centre of the circle, hence the term ‘centripetal’, which means ‘center seeking’.
The force that keeps an object moving in this circular path is the centripetal force.
It is also directed towards the centre of the circle. Therefore, it continually changes the direction of the object’s velocity to keep it moving in a circle.

The formula for centripetal acceleration is a = v^2 / r where ‘v’ denotes the speed and ‘r’ is the radius of the circle.
Centripetal Force can be calculated using the formula F = m * v^2 / r where ‘m’ refers to the mass of the object, ‘v’ is the speed and ‘r’ is the radius of the circle.
Both force and acceleration are proportional to the square of the speed as well as inversely proportional to the radius of the circular path.
Meaning, a greater speed or smaller radius increases centripetal force and acceleration, and vice versa.

Understanding uniform circular motion and concept of centripetal force and acceleration is crucial in various fields such as physics, astronomy and engineering.
Examples include the analysis of planetary orbits, design of roller coasters and motorway curves, and understanding the behaviour of electrons in a magnetic field.
It fundamentally underpins the principles of rotational mechanics.