An object moving at constant speed in a circle is always accelerating — its direction changes every instant, so its velocity changes even when its speed does not. This acceleration needs a force pointing towards the centre of the circle; that inward force is called the centripetal force.
Why is circular motion an acceleration even at constant speed?
Velocity is a vector quantity — it has both magnitude (speed) and direction. When an object moves in a circle at a steady speed, its speed is constant but its direction changes continuously. Because direction is part of velocity, the velocity is changing — and any change in velocity is, by definition, an acceleration.
This is the key conceptual hurdle in circular motion: you can accelerate without changing speed if you are changing direction.
From Newton's second law (F = ma), if there is an acceleration there must be a resultant force causing it. For circular motion, this force always points towards the centre of the circle — this is the centripetal force.
Centripetal means "centre-seeking" (from the Latin: centrum = centre, petere = to seek). The centripetal force is not a new type of force — it is the name given to whichever force (or resultant of forces) provides the inward acceleration for a particular circular motion.
What provides the centripetal force in different situations?
Centripetal force must be provided by something physical. Different situations use different forces as the centripetal force:
| Situation | What provides centripetal force |
|---|---|
| Moon orbiting Earth | Gravity (gravitational attraction between Moon and Earth) |
| Satellite orbiting Earth | Gravity |
| Car turning a corner on a flat road | Friction between tyres and road (directed towards centre of turn) |
| Ball on a string swung in a horizontal circle | Tension in the string |
| Object on a rotating fairground ride | Normal force from the seat/floor, directed inward |
| Electron orbiting a nucleus (Bohr model) | Electrostatic attraction between electron and proton |
| Banked road/track | Component of normal force directed towards centre |
A common error is to think there is an "outward" force on an object moving in a circle — this would be centrifugal force, which is not a real force in an inertial frame of reference. What you feel pressing you against the door of a car taking a sharp bend is the door pushing inward on you (the centripetal force); what you perceive as an outward push is simply your body's inertia trying to continue in a straight line. In GCSE, you do not need to include centrifugal force — it does not exist in a standard (inertial) reference frame.
How do you calculate centripetal force and acceleration?
The centripetal acceleration of an object moving in a circle of radius r at speed v is:
a = v² / r
The centripetal force required is:
F = mv² / r
Where:
- F = centripetal force (N)
- m = mass of the object (kg)
- v = speed of the object (m/s)
- r = radius of the circular path (m)
- a = centripetal acceleration (m/s²)
The centripetal acceleration and force always point towards the centre of the circle (inward).
Worked example:
A car of mass 800 kg travels around a roundabout of radius 20 m at a speed of 10 m/s. Calculate the centripetal force needed and identify what provides it.
Centripetal force = mv²/r = 800 × (10)² / 20 = 800 × 100 / 20 = 4,000 N
This force is provided by friction between the tyres and the road surface, directed towards the centre of the roundabout.
What happens if the centripetal force is removed?
If the centripetal force suddenly disappears — for example, if a string holding a spinning object breaks — the object no longer accelerates towards the centre. By Newton's first law, it continues in a straight line tangent to the circle at the point where the force was lost. It does not fly outward radially.
This is another classic exam misconception: when a spinning ball's string breaks, the ball flies off at a tangent, not straight outward.
How does changing speed or radius affect the required centripetal force?
From F = mv²/r, we can reason about the effect of each variable:
| Change | Effect on centripetal force required |
|---|---|
| Double the speed (v × 2) | Force increases by a factor of 4 (F ∝ v²) |
| Double the radius (r × 2) | Force halves (F ∝ 1/r) |
| Double the mass (m × 2) | Force doubles (F ∝ m) |
| Halve the radius (r ÷ 2) | Force doubles |
The v² relationship is the most important: small increases in speed require disproportionately large increases in centripetal force. This is why roads have lower speed limits on tight bends — the friction available from the tyres (which provides centripetal force) may not be sufficient at higher speeds, especially on wet roads.
How does circular motion apply to satellites?
For a satellite in a circular orbit, gravity provides the centripetal force:
Gravitational force = centripetal force
F_g = mv²/r
The speed of a satellite in a circular orbit at radius r around Earth can be derived from this relationship. Geostationary satellites orbit at a radius of about 42,000 km from Earth's centre (36,000 km above the surface), where the orbital period is exactly 24 hours — matching Earth's rotation. This allows them to remain stationary relative to a point on Earth's surface, making them ideal for communications and weather observation.
Frequently asked questions
Is centripetal force a real force?
Centripetal force is not an additional or separate force — it is the name we give to whichever real physical force (gravity, tension, friction, or a combination) acts towards the centre of a circular path. When you draw a free body diagram for an object in circular motion, you should label the real forces (gravity, normal force, friction, tension) and show that their resultant points towards the centre. You should not add an extra arrow labelled "centripetal force" as if it were a separate force acting on the object — that would be double-counting. The centripetal force equation F = mv²/r tells you how large the resultant inward force must be.
What is the difference between centripetal and centrifugal force?
Centripetal force is a real inward force acting on an object in circular motion, directed towards the centre. Centrifugal force is a fictitious outward force that appears to push objects away from the centre — but only in a rotating (non-inertial) reference frame. If you are sitting in a car going around a bend, you feel pressed outward against the door. From the perspective of someone standing outside watching, no outward force acts on you — the door simply exerts an inward (centripetal) force on you. The "outward push" you feel is the sensation of your inertia resisting the change of direction. In an inertial reference frame (the ground), centrifugal force does not exist. At GCSE, only centripetal force is needed.
Why do satellites not fall to Earth?
Satellites are falling — they are in constant free fall towards Earth under gravity. However, they are also moving horizontally at high speed. The curvature of Earth's surface means the ground curves away beneath the satellite at the same rate as it falls. The result is that the satellite falls around Earth rather than into it. The orbital speed at which this occurs for the International Space Station (at about 400 km altitude) is approximately 7,700 m/s — about 23 times the speed of sound. At this speed, gravity provides exactly the right centripetal force for a circular orbit at that radius.
How does banking a road help a car turn safely?
On a flat road, the centripetal force for turning is provided entirely by friction between the tyres and the road. If the road is icy or the speed is high, friction may be insufficient and the car slides outward. Banked roads (tilted inward on bends) allow the normal force from the road surface — which acts perpendicular to the road — to have a horizontal component directed towards the centre of the turn. This horizontal component contributes to the centripetal force, reducing the reliance on friction. At the correct "design speed" for a banked curve, no friction is needed at all; the normal force provides all the required centripetal force.
For predict-first GCSE physics with Professor Newton — predicting the direction of force before drawing the diagram — visit aitutors.me.