# 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 non-uniform, 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 non-inertial 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 non-uniform, involves acceleration. Even if the speed stays constant, the object is accelerating because its direction of motion is constantly changing.