🟢 Simulation physics · Level 2 · The Field

The pull that bends a path into a circle

Whirl a ball on a string and let go — it flies off straight, not outward. To keep anything moving in a circle, something must pull it constantly toward the centre. That inward pull is the centripetal force.

Always · toward the centreSize · F = mv²/rIn orbit · gravity supplies it7 question formats · layered hints

See it live

Matched pull — gravity gives exactly the inward force a circle needs
Too fast — the inward pull can't keep it circular, so the path stretches

The sun's gravity is the centripetal force here — always pointing inward. Get the speed right for the distance and it bends the path into a clean loop; too fast and the same pull only stretches it into an ellipse.

What's going on

What it is

Centripetal force is the net inward force that keeps an object moving along a curved path. It always points toward the centre of the circle, and its size is F = mv²/r — bigger for a faster speed or a tighter radius. It is not a new kind of force; it is the role played by whatever real force — gravity, tension, friction — happens to point inward.

How the principle works

By inertia, a moving object wants to travel in a straight line. To bend that path into a circle, a force must keep pulling it off the straight line, toward the centre. This inward force produces a centripetal acceleration a = v²/r, also pointing inward. Take the force away and the object instantly flies off along the tangent — a straight line, not outward.

How it works in Kinetica

In The Field the sun's gravity is the centripetal force. It tugs the disc inward every frame, bending its straight inertial path into a curve. Match the speed to the distance and the inward pull is exactly what a circle needs, so the disc loops in a steady orbit. Too slow and it spirals in; too fast and the orbit stretches into an ellipse.

Edge cases
  • Remove the force → the object flies off along the tangent (straight), not radially outward.
  • Faster speed or smaller radius → more centripetal force needed (F ∝ v², F ∝ 1/r).
  • Always perpendicular to the motion → it changes direction, never speed.
  • The outward "centrifugal" feeling → is apparent, just inertia felt in a turning frame.
Three points & measures
  • Centripetal force — F = mv²/r, always pointing inward.
  • Centripetal acceleration — a = v²/r, toward the centre.
  • The source — gravity, tension, friction, or a wall: whatever points to the centre.

The circular-motion laboratory

Centripetal force is easiest to feel when you can speed the spin up and watch the required pull grow — then cut the string and see the object fly off straight, not outward.

🎯 Ball-on-a-string sandbox

A ball circles a centre on a string. Speed it up and the inward pull the string must supply grows as . Push past what the string can hold and it snaps — and the ball leaves along the tangent.
Speed
0
Inward pull
0

The required pull is F = mv²/r — doubling the speed quadruples it. Cut the string and inertia carries the ball off in a straight line, the tangent, never straight out.

🤔 Guess before you reveal

You swing a ball on a string in a horizontal circle. At the top of the swing the string suddenly snaps. Which way does the ball fly?

🧪 Centripetal acceleration calculator — a = v²/r

The inward acceleration grows with speed squared and shrinks with radius. Try a car at v = 15 m/s on a bend of r = 30 m, and compare it with gravity (9.8 m/s²).

In the real world

A car rounding a bend

Friction between the tyres and the road provides the centripetal force that curves the car around a corner. Take the bend too fast and the friction can't supply enough inward pull, so the car skids straight on.

A spin dryer

The drum wall pushes the clothes inward, keeping them circling. The water isn't pulled in, so with nothing to bend its path it flies off straight through the holes — which is exactly how the spin gets clothes dry.

The Moon around Earth

Earth's gravity is the centripetal force holding the Moon in its near-circular orbit, constantly bending its straight-line motion into a loop. Without that inward pull, the Moon would simply drift off into space.

Glossary — the 10 words that unlock it

Centripetal force

What it means
The net inward force that keeps an object moving in a circle, F = mv²/r.
Why it matters
It is what bends straight-line motion into a curve; without it, no circular motion exists.
Example
A string pulling a whirling ball toward your hand.
Key question
Which way does centripetal force always point?

Centripetal acceleration

What it means
The inward acceleration of a circling object, a = v²/r, pointing to the centre.
Why it matters
Even at constant speed, changing direction is an acceleration — and it needs a force.
Example
A car on a roundabout accelerates inward the whole way around.
Key question
Can something accelerate without changing speed?

Circular motion

What it means
Movement along a circular path, often at a steady speed but ever-changing direction.
Why it matters
It is the setting for centripetal force, from orbits to spinning wheels.
Example
A stone whirled on a string traces circular motion.
Key question
What keeps circular motion from becoming a straight line?

Tangent

What it means
The straight line a circling object would follow the instant any inward force vanished.
Why it matters
It shows that released objects fly off straight, not outward — a common misconception.
Example
Sparks leaving a grinding wheel shoot off along the tangent.
Key question
In which direction does a released object actually travel?

Radius

What it means
The distance from the centre to the circling object; a tighter circle has a smaller radius.
Why it matters
Centripetal force grows as the radius shrinks (F ∝ 1/r), so tight turns pull harder.
Example
A short string makes a tighter, harder-pulling circle.
Key question
Does a smaller radius need more or less centripetal force?

Inertia

What it means
The tendency of a moving object to keep going straight at a steady speed.
Why it matters
It is exactly what the centripetal force must continually overcome to curve the path.
Example
A passenger leans outward as a car turns, trying to keep going straight.
Key question
What does centripetal force have to fight against?

Centrifugal force

What it means
The apparent outward push you feel in a turning frame; not a real force.
Why it matters
Naming it helps clear up why "outward" feelings are really just inertia.
Example
You feel flung outward on a fast merry-go-round.
Key question
Is the outward push in a turn a real force?

Period

What it means
The time taken for one complete trip around the circle.
Why it matters
It ties speed and radius together, and sets how fast the direction keeps changing.
Example
A satellite's period is how long one orbit takes.
Key question
What does the period of circular motion measure?

Tension

What it means
A pulling force transmitted through a string, rope, or cable.
Why it matters
It is one common supplier of centripetal force, as in a whirled ball.
Example
The taut string in a sling pulls the stone inward.
Key question
Name one real force that can act as centripetal force.

Banking

What it means
Tilting a road or track on a bend so the surface helps push vehicles inward.
Why it matters
It lets the normal force share the job of supplying centripetal force, so curves are safer at speed.
Example
Racetracks and motorway slip-roads are banked on tight curves.
Key question
Why are fast curves built with a tilt?

The physics, beyond the game

Centripetal force is the quiet inward pull behind every turn, orbit, and spin. This FAQ runs from whirling balls and cornering cars to satellites, spin dryers, and the reason "centrifugal force" is a comfortable fiction.

What is centripetal force in simple terms?
ConceptualWhatcomplexity 2

Centripetal force is the inward pull that keeps an object moving in a circle. The word means "centre-seeking": it always points toward the middle of the curve. Whirl a ball on a string and the string's pull is centripetal; remove it and the ball stops circling and flies off straight. Anything moving in a circle must have some inward force doing this job.

What is the formula for centripetal force, and what does it mean?
ConceptualWhatcomplexity 3

Centripetal force is F = mv²/r, where m is the object's mass, v is its speed, and r is the radius of the circle. The speed is squared, so going twice as fast needs four times the force. A smaller radius (tighter circle) also needs more force. The force points toward the centre, and the matching acceleration is a = v²/r.

Why does an object fly off in a straight line if the force stops?
ConceptualWhycomplexity 3

Because of inertia, a moving object keeps its velocity unless a force changes it. The centripetal force is the only thing bending the path into a circle. The instant that force disappears, nothing is left to curve the motion, so the object continues in the straight line it was travelling at that moment — the tangent to the circle, not a path straight outward.

What is the difference between centripetal and centrifugal force?
ComparativeWhatcomplexity 3

PropertyCentripetalCentrifugal
DirectionInward, to the centreOutward (apparent)
Real force?YesNo — a felt effect
CauseGravity, tension, frictionInertia in a turning frame
Acts onThe circling objectNothing real
The only real force in circular motion is centripetal, pointing inward; the outward "centrifugal" push is just inertia as felt by someone turning with the object.

Is centripetal force a new kind of force?
ConceptualWhethercomplexity 2

No — centripetal force is not a separate force of nature. It is a job description: whatever real force happens to point toward the centre is "acting centripetally". For a planet it is gravity, for a whirled ball it is the string's tension, for a turning car it is friction. The same familiar forces simply take on the centripetal role when they curve a path.

What provides the centripetal force when a car turns a corner?
ScenarioWhatcomplexity 3

Friction between the tyres and the road supplies it. As the car turns, the road pushes sideways on the tyres toward the centre of the bend, bending the car's path. If the road is icy or the speed too high, friction can't provide enough inward force, and the car slides straight on, unable to make the turn. Banking the road can help by adding to the inward push.

Why does a faster or tighter turn feel stronger?
ScenarioWhycomplexity 3

Because centripetal force grows with v²/r. Doubling your speed quadruples the inward force needed; halving the radius doubles it. A fast, tight turn therefore demands a large inward force, which your body feels as a strong sideways press against the seat or door. That pressing sensation is your own inertia resisting the change of direction the force is imposing.

How does gravity act as a centripetal force for the Moon and satellites?
ScenarioHowcomplexity 4

Gravity pulls the Moon (or a satellite) straight toward Earth's centre, exactly the direction a centripetal force must point. The Moon's sideways speed would carry it off in a straight line, but gravity continually bends that line into a near-circle. The orbit is a perfect balance: the inward gravitational pull provides just the centripetal force needed for the Moon's speed and distance.

Why does water fly out of a spinning washing machine?
ScenarioWhycomplexity 3

The drum wall pushes the clothes inward, giving them the centripetal force to keep circling. The water, sitting in the fabric, has no such inward force once it reaches the holes — so, by inertia, it travels straight on and escapes through the openings. The spin does not throw the water out; it simply lets the water continue straight while the clothes are held in.

How can there be acceleration if the speed stays constant?
ConceptualHowcomplexity 4

Acceleration means any change in velocity, and velocity includes direction as well as speed. In circular motion the speed can be perfectly steady while the direction changes every instant — and changing direction is itself an acceleration. That acceleration, a = v²/r, points toward the centre, which is why a centre-seeking force is required even for a steady circle.

Why are racetracks and roads banked on curves?
ScenarioWhycomplexity 3

Banking tilts the surface so it pushes vehicles partly toward the centre of the bend. This lets the road's normal force share the job of supplying centripetal force, instead of relying on friction alone. As a result, vehicles can take the curve faster and more safely, and the design is gentler on tyres. Steeply banked velodrome and motorway curves use exactly this trick.

Does centripetal force do any work on the object?
ConceptualWhethercomplexity 4

No. Work is done only when a force has a component along the motion. Centripetal force points toward the centre, exactly perpendicular to the object's velocity, so it never speeds the object up or slows it down — it only turns it. That is why an object can circle at constant speed indefinitely under a centripetal force without gaining or losing energy.

What happens if the centripetal force is too small or too large?
ConceptualWhatcomplexity 3

If the inward force is too small for the speed and radius, the path can't curve tightly enough, so the object spirals outward or flies off. If it is larger than needed, the path curves more sharply, tightening into a smaller circle or pulling the object inward. A stable circle exists only when the available inward force exactly matches the mv²/r that the motion requires.

How is centripetal force related to Newton's laws?
ConceptualHowcomplexity 3

It is Newton's laws applied to a curved path. Newton's first law says the object would go straight without a force; Newton's second, F = ma, gives the size of the inward force as F = mv²/r, since the centripetal acceleration is v²/r. So centripetal force is not a new rule but the familiar laws of motion describing what it takes to keep turning.

Where do we meet centripetal force in everyday life and technology?
ReflectiveWhycomplexity 4

Everywhere things turn. It steers cars around bends and trains around curves, holds satellites and the Moon in orbit, spins water from laundry and separates samples in a centrifuge, and presses you into your seat on a fairground ride. Engineers size it carefully — banking roads, strengthening rotor blades, planning orbits — because getting the inward force right is what keeps circular motion safe and stable.

Test yourself — a mixed set

Seven question formats, the way Beyond Dictionary serves them. Every question has layered hints — a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 32 questions across all seven formats — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own.

Question 1 of 32
MCQ

Key takeaways

  • Centripetal force is the inward pull that bends motion into a circle: F = mv²/r.
  • It always points toward the centre, perpendicular to the motion.
  • Remove it and inertia sends the object straight along the tangent — not outward.
  • It is a role filled by gravity, tension, or friction — not a new kind of force.
  • The outward "centrifugal" feeling is apparent; the real force is centripetal, inward.

🪜 Where this lesson leads

Centripetal force is the key to every kind of turning. Grasp it and you have started climbing toward:
Inertia
Force (F = ma)
Circular motion
Centripetal acceleration
Gravity as centripetal
Orbits & satellites
Banked curves & g-forces
Rotating machinery

Keep exploring

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