Circular Motion
Circular Motion Basics

Circular motion refers to the movement of an object along the circumference of a circle or rotation along a circular path.

It can be uniform, with a constant angular rate, or nonuniform, with a changing rate of rotation.

The rotating object maintains a constant distance from a central point, often termed the centre of rotation.

Circular movement is a result of a centripetal force, directing toward the centre and causing the object to follow a circular path.
Centripetal Force

Centripetal force is a force that makes a body follow a curved path—specifically in a circular path.

Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous centre of curvature of the path.

Centripetal force is calculated using the formula: F = mv^2/r, where:
 m = mass of the object,
 v = velocity of the object,
 r = radius of the circular path.
Centrifugal Force

In some cases, you may come across the concept of centrifugal force.

Centrifugal force is often considered a “fictitious” force. It does not come into play when analysing an object’s motion from an inertial reference frame.

However, it’s sometimes useful when analysing motion from a rotating perspective (a noninertial reference frame).

You may think of it as an “outward force” that balances the centripetal force in a rotating system.
Angular Velocity and Acceleration

Angular velocity is the rate of change of an angle with respect to time. It is represented as ω and given by the formula: ω = Δθ/Δt.

Angular acceleration is the rate of change of angular velocity with respect to time. It is represented as α and is given by the formula: α = Δω/Δt.
Tangential Velocity and Acceleration

Tangential velocity is the linear speed of any object moving along the circular path. It is perpendicular to the radius of the path.

Tangential acceleration is the rate of change of the tangential velocity. It points along the curve in the direction of the velocity vector.
Some Practical Circular Motion Scenarios

In reality, many motions are circular, such as the rotation of planets around stars, electrons around nuclei, and cars rounding bends.

It’s crucial to understand that circular motion, whether uniform or nonuniform, involves acceleration. Even if the speed stays constant, the object is accelerating because its direction of motion is constantly changing.