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 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.