# 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.

## Centripetal Force and Acceleration

• 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.

## Calculating Centripetal Acceleration and Force

• 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.

## Applications and Implications

• 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.