Circular motion: why centripetal force is not a new force
Ask a Year 13 student to draw the forces on a conker being whirled round on a string, and a surprising number will draw three arrows: the weight, the tension, and a third one labelled “centripetal force”. It looks thorough. It’s wrong, and the examiner takes marks off for it. That extra arrow is the mistake I see most often in circular motion, and once it’s gone most of the topic falls into place.
In this guide
Centripetal force is a job title
Here is the idea in one line: centripetal force is not a type of force. It’s a description of what some other force is doing.
Gravity, tension, friction, the push of a surface: those are forces. Any of them can end up pointing at the centre of a circle, and when it does, it’s the centripetal force in that situation. The word describes a direction and an effect. It doesn’t add anything to the diagram.
Think of the word “goalkeeper”. It tells you what one player is doing, but nobody counts the goalkeeper as a twelfth player on top of the eleven. A student who draws the extra arrow is counting the goalkeeper twice.
OCR’s specification puts it carefully: a constant net force perpendicular to the velocity of an object makes it travel in a circle. Net is the important word. Centripetal force is the resultant of the real forces, found after they’re drawn, not one more force to add to the list.
So the question your child should ask every time is this: what is actually providing the centripetal force here? For the conker, it’s the tension in the string. For a car going round a roundabout, it’s friction between the tyres and the road. For the Moon, it’s the Earth’s gravity. Once they can answer that, the equation almost writes itself.
Constant speed, and still accelerating
This part sounds like a trick, and it bothers good students more than weak ones.
An object going round a circle at a steady speed is accelerating. That seems to contradict everything from GCSE, where acceleration meant speeding up or slowing down. The way out is that A-Level Physics defines acceleration as a change in velocity, and velocity includes direction. A car on a roundabout at a constant 20 miles per hour is changing direction all the time, so its velocity is changing all the time, so it’s accelerating.
The acceleration points towards the centre of the circle, and its size is a = v²/r. Multiply by the mass and you get the resultant force needed to hold the object on that circle: F = mv²/r. Both are printed in OCR’s Data, Formulae and Relationships booklet, which your child has in the exam, along with the versions written in terms of angular velocity.
What the booklet can’t do is tell your child which force to set equal to mv²/r. That’s the physics, and it’s where the marks are.
Radians, and the calculator in the wrong mode
Circular motion is where A-Level Physics stops letting students use degrees. Angles are measured in radians, with one full turn being 2π radians, and the angular velocity ω (the Greek letter omega) is the angle swept out each second. The booklet gives ω = 2π/T and ω = 2πf, where T is the time for one turn and f is the number of turns per second, and it links the two kinds of speed with v = ωr.
None of that is hard on paper. The problem is the calculator.
A calculator left in degrees mode gives a confident, wrong answer to any question that takes the sine or cosine of an angle in radians, and nothing on the screen warns you. It’s one of the commonest ways I see marks go missing in this part of the course. Checking for the small D or R at the top of the display takes a second, and the habit is worth building now rather than in the exam hall. It matters even more in the next topic, simple harmonic motion, where every equation runs in radians.
The questions that catch students out
Most circular motion questions are one of three kinds, and each has its own trap.
The first is the horizontal circle: a car on a flat bend, or a coin on a turntable. One real force does the job, usually friction, so friction equals mv²/r. The trap is the extra arrow again.
The second is the vertical circle, usually a ball on a string swung over the top. At the top of the loop, the weight and the tension both point down, towards the centre, so together they provide the centripetal force: T + mg = mv²/r. At the bottom, the tension points up and the weight points down, so the resultant is T − mg. Students who learn one of those and use it for both positions lose the marks. There’s a classic follow-up too. The slowest speed at which the string stays tight at the top is the speed at which the tension falls to zero, so mg = mv²/r and v = √(gr).
The third kind is written. OCR likes to ask students to explain why an object moves in a circle, and the word “centrifugal” in that answer is a reliable way to lose the mark. Your child should write about a resultant force towards the centre, at right angles to the velocity, and name the real force providing it.
The specification also names a practical: investigating circular motion with a whirling bung. A rubber bung on a string is spun in a horizontal circle above the head, the string runs down through a tube, and weights hanging from the bottom of the string set the tension. Questions on it ask what was measured and how the uncertainty could be reduced, so it’s worth your child knowing how it works even if their class never did it.
Why this topic keeps coming back
Circular motion sits in Module 5 of OCR A-Level Physics A. That means it can appear on Paper 1 (Modelling physics) and on Paper 3 (Unified physics), the paper that draws on the whole course. It doesn’t stay in its own chapter, either.
Gravitational fields, a few weeks later, is circular motion with gravity as the centripetal force. Set the gravitational force equal to mv²/r and out comes the link between a satellite’s orbit radius and its period, which is a staple of the exam. A student who still thinks of centripetal force as an extra force will draw the extra arrow there too.
That’s why I’d rather fix the idea properly now than patch individual questions later. My guides on simple harmonic motion and gravitational fields and orbits pick up exactly where this one stops.
One question you can ask at the dinner table
You don’t need any physics to check whether this idea has landed. Pick anything that goes round in a circle and ask your child what’s providing the centripetal force.
A child on a playground roundabout: the grip of their hands, pulling them inwards. A washing machine drum on its spin cycle: the drum wall, pushing the clothes inwards. (That’s also why the water leaves through the holes, since nothing pushes the water inwards once it reaches one.) The International Space Station: the Earth’s gravity. A car on a motorway slip road: friction from the road surface.
If the answer comes back as the name of a real force, they’ve got it. If it comes back as “centripetal force”, ask again. That’s the extra arrow, said out loud.
It takes a minute, and it does more good than an evening of copying notes.
Common questions
Is centripetal force a real force?
Not a separate one. Centripetal force is the name for the resultant force towards the centre of a circle, and a real force such as tension, friction or gravity always provides it. Drawing it as an extra arrow on a force diagram counts that force twice and loses marks.
Why do A-Level Physics students use radians for circular motion?
Because the equations that link angle, speed and time, such as v = ωr, only work with angles in radians. One full turn is 2π radians. Students should check their calculator is in radians mode before any question that takes a sine or cosine.
Which OCR A-Level Physics papers test circular motion?
Circular motion is in Module 5 of OCR A-Level Physics A, so it can be examined on Paper 1, Modelling physics, and on Paper 3, Unified physics, which covers all six modules. It also comes back inside gravitational fields, where gravity provides the centripetal force on an orbiting satellite.