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 string | Tension in the string |
| Car turning a corner | Friction between tyres and road |
| Planet orbiting a star | Gravity |
| Electron orbiting nucleus | Electrostatic attraction |
| Roller coaster loop | Normal 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)
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 minutes | ISS, spy satellites |
| Geostationary | 35,786 km | 24 hours | TV, 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)