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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.
Note 
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