Centripetal Force

Centripetal force — the resultant force causing circular motion, directed towards the centre.

F = mv² / r = mω² r

It is not a new kind of force — this is the single most important point in the topic. "Centripetal" describes the role a force is playing, not its origin. In any given situation some ordinary force is providing it:

A car on a bend — friction between tyres and road.

A planet orbiting a star — gravitational attraction.

A ball on a string whirled horizontally — tension in the string.

A passenger on a fairground ride — the normal contact force from the wall or seat.

Example: a free-body diagram should never show a separate arrow labelled "centripetal force" alongside tension or friction. That would be counting the same force twice. Identify the real forces, then say which of them, or which component, provides the centripetal force.

Cut the string and the object goes straight — it does not fly outwards along the radius. With no resultant force it continues in a straight line, tangential to the circle at the moment of release, exactly as Newton's first law requires. This is a common exam question and a common wrong answer.

Example: a 1200 kg car rounding a bend of radius 50 m at 15 m s⁻¹ needs F = 1200 × 15² ÷ 50 = 5400 N, supplied by friction. If the road is icy and friction cannot supply 5400 N, the car cannot follow that path and travels along a straighter one — it does not slide outwards along the radius.

No work is done by a centripetal force — it acts perpendicular to the velocity at every instant, and W = Fs cosθ with θ = 90° gives zero. This is why a satellite in a circular orbit neither gains nor loses kinetic energy, and why whirling a ball on a string requires no continuous energy input once it is moving.