🌍

Circular Motion

Year 11 (IGCSE) 🚀 Forces & Motion  Explain centripetal force and acceleration; apply to orbits.

⭕ Centripetal Acceleration and Force

An object moving in a circle is constantly changing direction. This means its velocity is always changing — so there must be an acceleration (even at constant speed!).

⭕ Centripetal Acceleration
$$a = \frac{v^2}{r} \qquad F = \frac{mv^2}{r}$$

The centripetal force always points towards the centre of the circle

🎯 "Centripetal" means "centre-seeking". There is no outward "centrifugal force" — that's just your inertia making you feel pushed outward in a turning car!

📐 F = mv²/r in Context

The centripetal force isn't a new type of force — it's just the name for the resultant force pointing towards the centre. In different situations, different forces provide it.

🔄 Scenario🎯 What provides centripetal force
Ball on a stringTension in the string
Car turning a cornerFriction between tyres and road
Planet orbiting a starGravity
Electron orbiting nucleusElectrostatic attraction
Roller coaster loopNormal force + weight
🚗 Example: A 1000 kg car travels at 20 m/s around a bend of radius 80 m.
F = mv²/r = 1000 × 400 / 80 = 5000 N (provided by road friction)

🌍 Orbital Motion and Satellites

For a satellite orbiting at radius r with orbital speed v, gravity provides the centripetal force.

🛸 Orbital Speed
$$\frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow v = \sqrt{\frac{GM}{r}}$$
🛸 Orbit type📍 Height⏱️ Period🔍 Used for
Low Earth Orbit (LEO)200–2000 km~90 minutesISS, spy satellites
Geostationary35,786 km24 hoursTV, weather, communication
📡 A geostationary satellite orbits exactly in sync with Earth's rotation — from the ground it appears completely stationary, which is why your satellite TV dish always points the same direction!
🎯 Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
⚗️ ⭕ Centripetal Force Calculator (F = mv²/r)