Centripetal Force

Centripetal force is the name for the pull that keeps an object moving in a circular path. Without it, the object would fly off in a straight line. The Moon stays in orbit around Earth because gravity provides the centripetal force. A car turning a corner stays on the road because friction with the tyres provides the centripetal force. A spinning conker on a string stays in its circle because the tension in the string provides the centripetal force. Anything moving in a circle needs centripetal force pointing towards the centre of the circle.

  • What it doesKeeps things going in a circleAlways points to centre
  • Without itObject flies off in a straight lineNewtons first law
  • Famous examplesOrbits, turning cars, conkersPlus rollercoasters
  • FormulaF = m v^2 / rMass, speed squared, divided by radius
  • More speedMore force neededSquared dependence
  • Smaller circleMore force neededTighter turn, harder pull

What is centripetal force?

The word centripetal means "centre-seeking". A centripetal force always points from the moving object towards the centre of the circle it is moving around.

Without this force, an object would obey Newtons first law and continue in a straight line. Adding a constant pull towards the centre bends the straight line into a curve, eventually a complete circle.

Examples of centripetal force

  • The Moon orbiting Earth: gravity pulls the Moon constantly toward Earths centre. Without that pull, the Moon would fly off in a straight line and disappear into space.
  • A car turning a corner: friction between the tyres and the road pushes the car towards the centre of the turn. On ice or in heavy rain, friction drops and the car may skid in a straight line off the road.
  • A conker on a string: the string pulls the conker towards your hand, keeping it spinning in a circle. Let go and the conker flies off in whichever direction it was moving at that instant.
  • A bicycle going round a banked track: the angled track provides centripetal force by tilting the riders weight inward.
  • Clothes in a tumble dryer: the rotating drum pushes the wet clothes towards the centre (sort of); water can pass through the drum walls but the clothes cannot, so water flies out by the holes and clothes are flung against the wall.
  • A roller coaster loop: the rails push the cars (and you) inwards as you go around the loop.
  • A planet orbiting the Sun: again, gravity provides the centripetal force.
Fact If gravity suddenly switched off, the Moon would NOT fall down to Earth: it would fly off in a straight line, tangent to its current orbit. It would shoot away from us at about 1 km per second and would never come back. Gravity is the centripetal force that constantly bends its straight-line motion into the curved orbit we see.

The formula

The size of centripetal force needed is:

F = m v^2 / r

Where F is force, m is mass, v is speed, and r is the radius of the circle. Three things to notice:

  • More mass = more force needed (a heavy car needs more grip than a light one).
  • More speed = MUCH more force needed (speed squared; doubling speed quadruples the force).
  • Smaller radius = more force needed (a tighter turn is much harder).

Why cornering fast is dangerous

Because force grows as the square of speed, a car at 60 km/h needs 4 times the centripetal force of a car at 30 km/h to turn the same corner. A car at 90 km/h needs 9 times the force. Tyres can only provide so much grip. If you try to turn a corner faster than the tyres can grip, you skid in a straight line off the road.

That is why country roads have signs recommending lower speeds for sharp bends and why race tracks are carefully designed for the speeds cars will reach there. It is also why mountain roads slope inwards on tight turns (called banking), so that part of the cars weight provides centripetal force, helping the tyres.

Why riders lean inwards

You may have noticed that cyclists, motorcyclists and runners all lean into a turn. The reason is centripetal force.

The centripetal force has to point from the rider towards the centre of the turn (which is sideways, parallel to the ground). The riders weight pulls straight down. By leaning inward, the rider lines up these two forces so they balance correctly through the riders body. A rider not leaning would feel the force trying to push their top half outward, threatening to tip them over the outside of the turn.

In a banked velodrome track, the track is tilted inward so steeply that the riders body is almost level with the ground at the corners, all forces balanced perfectly.

Did you know? A famous quirky illusion: there is no such force as centrifugal force in real physics (although the word is sometimes used loosely). The feeling of being "thrown outwards" in a turning car is just your bodys inertia trying to continue in a straight line, while the car curves underneath you. The only real force is the centripetal force pulling you inward. The "outward" feeling is what physicists call a pseudo-force: real to you in the rotating frame, but not really there.

Roller coaster loops

One of the most famous demonstrations of centripetal force is a roller coaster loop. As your car climbs up the inside of the loop, the track curves so sharply that the rails actually have to push your car (and you) inwards, towards the centre of the loop. At the top, you are upside down, but the rails are pushing down on you (which means towards the centre of the loop, which happens to be below you at that point). The centripetal force keeps you safely against your seat throughout.

The exciting part is that you feel an extra "weight" at the bottom of the loop (where the rails push you up against gravity) and feel almost weightless at the top of the loop (where the centripetal force exactly equals what gravity is trying to do). The full circle is engineered so that even the slowest moments of the ride still have enough speed to keep the car safely against the rails.

Try this Fill a bucket about a third full of water. Holding the handle, swing it carefully around in a vertical circle. As long as you swing fast enough, the water stays in the bucket even when it is upside down at the top of the swing. The centripetal force from the swinging bucket pushes the water inwards (which at the top is downwards into the bucket), keeping it in place. Slow down too much and the water falls out (suddenly there is not enough centripetal force, so gravity wins).
Deeper dive: spinning to make artificial gravity in space

One of the biggest challenges of long space missions is weightlessness. Without gravity, astronauts bones and muscles weaken, hearts shrink, fluids shift around the body. Engineers have long dreamed of producing artificial gravity in space ships using centripetal force.

The basic idea: build a spinning section of the spacecraft. As you stand on the inside of the spinning wall, the centripetal force pushes you outward (into the wall) just as gravity pushes you down on Earth. To you it feels like normal gravity, with the spinning wall acting as the floor. Designs from the 1960s show ring-shaped spacecraft that would rotate slowly to give astronauts inside a steady "gravity" of around 1g.

The challenge is engineering. To produce 1g of artificial gravity, you need a spinning radius of around 224 metres (turning once per minute), or 90 metres (turning twice per minute). Smaller spacecraft would have to spin much faster, which can produce unpleasant side effects: differences in apparent gravity between your feet and your head, and a sense of dizziness when turning your head.

So far, no spacecraft has been built with rotating sections for crew comfort. The International Space Station rotates around Earth, but the whole station is in free fall together: astronauts inside still feel weightless.

Several private companies are now designing the first practical rotating space habitats, with NASA studying possible Mars-mission designs that include a slowly rotating crew section. If humans ever build cities in space or settle Mars, centripetal force may be the key to giving people the gravity their bodies need.

For more, see gravity and Newtons three laws of motion.