Circular Motion

Uniform Circular Motion

An object rotating at a steady rate, where the speed is constant but the direction is changing.

Angular Speed (w)

The rate at which an object rotates, measured in radians per second, given by w = 2π / T or w = 2πf.

Centripetal Acceleration

The acceleration directed towards the center of a circular path, necessary for an object to maintain circular motion.

Centripetal Force

The resultant force acting towards the center of a circle that keeps an object moving in circular motion.

Resultant Force (F) on a vehicle at the top of a hill

The difference between the weight (mg) and the support force (S) acting on the vehicle.

Threshold Velocity (v0)

The speed at which a vehicle loses contact with the ground at the top of a hill, given by v₀² = gr.

Force of Friction (F) on a roundabout

The frictional force providing centripetal force, given by F = mv² / r.

Support Force at the Bottom of a Dip

The force acting upwards against weight, providing centripetal force during circular motion.

Energy Conservation in a Swing

At the bottom of the swing, kinetic energy (1/2mv²) is converted to gravitational potential energy (mgh).

Centripetal Force at the Big Wheel

The sum of the reaction force (R) and weight (mg) at maximum height, given by R + mg = mv² / r.