PhysicsICSE Class 10 · Uniform Circular Motion

Centripetal Force: What Provides It and Why It Does No Work (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Centripetal force is the force, directed along the radius towards the centre, that keeps a body moving in a circle. It is a real force supplied by an agent: tension in a string, gravity for a satellite, friction for a turning car. It is always at right angles to the motion, so it does no work.

The inward force is at 90° to the velocity, so it only turns the stone and does no work; if the string breaks, the stone leaves along the tangent.

Illustration drawn for QuestionBuddy.

Understand Centripetal Force: Sources and Work Done

A body moving in a circle is accelerated, because the direction of its velocity keeps changing. By Newton's second law an acceleration needs a net force. For uniform circular motion that force is the centripetal force ('centre-seeking'): a force directed along the radius towards the centre of the circle.

It is a real force with a source. The name describes the job, not a new kind of force. In each case something real supplies it:

a stone whirled on a string: the tension in the string;
the Moon round the Earth, the Earth round the Sun, an artificial satellite: gravitational attraction;
a car or cyclist turning on a level road: friction between the tyres and the road;
an electron round the nucleus: electrostatic attraction;
clothes in a spinning drum, a bead on a circular wire: the push of the wall (normal reaction).

Without it, no circle. If the centripetal force stops (the string breaks, the road is too slippery), nothing pulls the body inwards, so by Newton's first law it continues in a straight line along the tangent at the point where it was. It does not fly outwards along the radius. That is why sparks leave a grinding wheel along tangents and why a car on ice skids off the curve.

More force for faster or tighter turns. For the same body, a larger centripetal force is needed if the speed is larger or the circle is smaller. A car can take a bend at low speed but skids at high speed when friction can no longer supply enough force. (You only need this idea qualitatively; the ICSE Class 10 syllabus has no centripetal-force formula.)

It does no work. At every instant the centripetal force is along the radius and the displacement is along the tangent. The angle between them is $90°$ , so

$W = F s cos 90° = 0.$

So the centripetal force does not change the speed or the kinetic energy of the body. This is why a satellite can keep circling at constant speed without burning fuel, and why, in the 2024 paper, the expected answer for the work done by the string's tension on a whirled stone was 'zero, because the force is perpendicular to the displacement at every instant'. The reason is the right angle, not that the stone returns to its starting point.

Diagram to remember. At any point P on the circle, draw velocity along the tangent and the centripetal force from P towards the centre O: the two arrows are perpendicular.

Centripetal Force: Sources and Work Done: formulas and key facts

Work by the centripetal force: $W = F s cos 9 0^{\circ} = 0$; Force along the radius, displacement along the tangent.
Kinetic energy in uniform circular motion: $K = \frac{1}{2} m v^{2} = constant$; No work is done on the body, so its kinetic energy does not change.
Speed on the circle: $v = \frac{2 π r}{T} = 2 π r n$; $n$ = revolutions per second.
Direction rule: $F_{c} ⊥ v$; Centripetal force towards the centre; velocity along the tangent.

How to solve Centripetal Force: Sources and Work Done questions

Most centripetal-force questions ask 'what provides it?', 'what does it do?' or 'what happens without it?'.

1Identify the centre of the circle and the body moving round it.
2Ask which real force on the body points towards that centre: tension, gravity, friction, electrostatic attraction or a wall's push.
3Name it as 'centripetal force, provided by …'.
4For work done, state that the force is perpendicular to the displacement at every instant, so $W = F s cos 90° = 0$ .
5For 'what if it stops?', the body moves along the tangent at that point (Newton's first law).
6For numericals, find speed from $v = \frac{2 π r}{T}$ and kinetic energy from $\frac{1}{2} m v^{2}$ ; the work by the centripetal force is always zero.

Centripetal Force: Sources and Work Done in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Tension does no work

Suppose you whirl a key-ring of mass 0.2 kg on its strap in a horizontal circle of radius 0.5 m, making 2 revolutions every second.

Find its speed ( $π = 3.14$ ), its kinetic energy, and the work done by the strap's tension in 10 s.

Try it first, then show the solutionSolution

$v = 2 π r n = 2 \times 3.14 \times 0.5 \times 2 = 6.28$ m/s.
$K = \frac{1}{2} \times 0.2 \times 6.2 8^{2} \approx 3.94$ J.
Tension is towards the centre, at $90°$ to the motion at every instant, so its work is zero in 10 s, or in any time.

Answer: 6.28 m/s; about 3.94 J; zero work.

Memory hook: Pulling sideways steers; it never speeds up or slows down.

Let go and go straight

Imagine a child on a merry-go-round holding a rail. The rail pulls her towards the centre as she goes round.

What provides her centripetal force, and in which direction does she move if she lets go?

Try it first, then show the solutionSolution

The pull of the rail through her arms (a real push or pull from the rail) provides the centripetal force.
If she lets go, nothing pulls her inwards, so she moves in a straight line along the tangent at that point.

Answer: The rail's pull; along the tangent, not straight outwards.

Memory hook: No pull to the centre, no curve.

Tricks to remember Centripetal Force: Sources and Work Done

Short memory aids. Say each one aloud once, then use it on a question the same day.

Centre-seeking
Centri-petal: 'centre-seeking'. It always points to the centre.
Use it when: Direction questions; do not confuse with centrifugal ('centre-fleeing').
T-G-F-E
Tension, Gravity, Friction, Electrostatic: the usual suppliers of centripetal force.
Use it when: 'What provides the centripetal force?' questions.
Ninety means nothing
Force at 90° to motion: cos 90° = 0, so no work, no change in speed.
Use it when: Work-done questions like 2024 Q2(ii)(b).
Tangent on release
When the pull stops, the body leaves along the tangent, like a car going straight on at a bend.
Use it when: String-breaks and skidding questions.

Centripetal Force: Sources and Work Done: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: A cyclist on a bend · 1 mark · MCQBoard level

A cyclist goes round a bend on a level road at constant speed. The centripetal force on the cyclist and cycle is provided by:
(a) the weight of the cyclist
(b) friction between the tyres and the road
(c) the centrifugal force
(d) the pedalling force

Try it first, then show the solutionSolution

On a level road, the only horizontal force from the road towards the centre of the bend is friction on the tyres.
Centrifugal force is not a real force and cannot supply anything.

Answer: (b)

Example 2: Matching the source · 2 marks · Short answerBoard level

Match each motion with the force that provides its centripetal force: (i) the Earth going round the Sun, (ii) a hammer whirled on a wire, (iii) a car turning on a flat road, (iv) an electron going round a nucleus. Forces: friction, electrostatic attraction, tension, gravitational attraction.

Try it first, then show the solutionSolution

(i) Gravitational attraction of the Sun. (½) (ii) Tension in the wire. (½)
(iii) Friction between tyres and road. (½) (iv) Electrostatic attraction of the nucleus. (½)

Answer: (i) Gravitational attraction (ii) Tension (iii) Friction (iv) Electrostatic attraction

Example 3: Work and energy for a whirled stone · 3 marks · Short answerHarder board level

A stone of mass 0.5 kg is whirled in a horizontal circle of radius 1 m at a constant speed of 4 m/s and makes 10 revolutions. ( $π = 3.14$ )
(a) How much work does the tension do in the 10 revolutions? Give a reason.
(b) Find the kinetic energy of the stone.
(c) Find the distance travelled.

Try it first, then show the solutionSolution

(a) Zero: the tension acts towards the centre, perpendicular to the displacement at every instant, so $W = F s cos 90° = 0$ . (1)
(b) $K = \frac{1}{2} \times 0.5 \times 4^{2} = 4$ J, and it stays 4 J throughout. (1)
(c) $10 \times 2 π r = 10 \times 2 \times 3.14 \times 1 = 62.8$ m. (1)

Answer: (a) Zero (b) 4 J (c) 62.8 m

Example 4: Which way do the sparks go? · 2 marks · Short answerHarder board level

A knife is held against the top of a grinding wheel that turns clockwise as you look at it. In which direction do the sparks leave the top of the wheel? Explain why they do not fly straight upwards.

Try it first, then show the solutionSolution

Turning clockwise, a point at the top of the wheel moves to the right, so its velocity there is horizontal, to the right (the tangent at the top). (1)
Once a hot particle breaks free, no centripetal force acts on it, so it continues along that tangent (horizontally to the right), not along the radius (upwards). (1)

Answer: Horizontally to the right, along the tangent at the top; there is no outward force to throw them radially.

Example 5: A faster car on the same curve · 3 marks · Short answerHOTS / competency

A car takes a curve on a level road safely at 30 km/h. On another day, it takes the same curve at 60 km/h and skids.
(a) What provides the centripetal force?
(b) Why does the car skid at the higher speed?
(c) In which direction does it skid, and why is this not 'outwards along the radius'?

Try it first, then show the solutionSolution

(a) Friction between the tyres and the road. (1)
(b) A faster turn on the same curve needs a larger centripetal force; friction has a maximum value and cannot supply that much, so the car cannot follow the curve. (1)
(c) With too little inward force, the car tends to keep going in a straight line along the tangent, so it slides towards the outer edge of the curve. No outward force pushes it; it simply fails to turn enough. (1)

Answer: (a) Friction (b) The needed centripetal force exceeds the friction available (c) Along the tangent, drifting to the outside of the curve.

Example 6: Case study: a space station · 4 marks · Case-basedHOTS / competency

A space station orbits the Earth in a circle of radius 6800 km, taking 90 minutes per orbit. Its engines are off. ( $π = 3.14$ )
(a) What provides its centripetal force?
(b) Find its speed in km/s, to one decimal place.
(c) Why does it not need fuel to keep its speed?
(d) What would happen if the Earth's pull suddenly vanished?

Try it first, then show the solutionSolution

(a) The Earth's gravitational pull on the station. (1)
(b) $v = \frac{2 π r}{T} = \frac{2 \times 3.14 \times 6.8 \times 1 0 ^{6}}{90 \times 60} \approx 7908$ m/s $\approx 7.9$ km/s. (1)
(c) Gravity acts towards the Earth's centre, at right angles to the motion, so it does no work; the kinetic energy and speed stay the same. (1)
(d) It would move off in a straight line along the tangent to the orbit at that point. (1)

Answer: (a) Earth's gravity (b) About 7.9 km/s (c) Gravity does no work on it (d) It moves along the tangent.

Where students lose marks in Centripetal Force: Sources and Work Done

The slips examiners see most often, and what to write instead.

Mistake: Naming the wrong force
The force needed for circular motion is called the centripetal force; tension is what provides it in the case of a string.
Wrong working
The tension provides 'rotational force' (or 'tension force') for circular motion.
Right working
The tension provides the centripetal force.
Do this: Write 'centripetal force, provided by …'.
Usually costs: Reported for 2024 Q2(ii)(a).
Mistake: Giving a non-zero work, or zero for the wrong reason
Work is zero because the force is perpendicular to the displacement at every instant.
Wrong working
Work is constant; or $W = F \times s$ ; or zero because the displacement in one round is zero.
Right working
$W = F s cos 90° = 0$ at every instant.
Do this: Always quote the right angle between force and displacement.
Usually costs: Reported for 2024 Q2(ii)(b).
Mistake: Saying the body flies outwards when the force stops
No outward force acts; the body continues along the tangent by inertia.
Wrong working
When the string breaks, the stone flies away from the centre along the radius.
Right working
It moves along the tangent at the point where the string broke.
Do this: Draw the tangent at the point of release.
Usually costs: The reasoning mark in 2-3 mark questions.
Mistake: Listing centrifugal force as a provider
Centrifugal force is an apparent force in the rotating frame; it cannot provide the centripetal force.
Wrong working
Centrifugal force balances centripetal force and keeps the body in the circle.
Right working
A real force (tension, gravity, friction) provides the centripetal force; nothing balances it.
Do this: Remember: a body in circular motion is not in equilibrium; it is accelerating.
Usually costs: MCQ and reasoning marks.

Exam tips

The 2024 paper asked, as a fill-in, what the tension provides and the work it does; the expected answers were 'centripetal' and 'zero (force perpendicular to displacement)'.
When asked 'what provides the centripetal force', name the real force and the agent: 'gravitational pull of the Earth', 'friction between tyres and road'.
In diagrams, draw the velocity along the tangent and the force towards the centre at the same point.
No formula for centripetal force is in the 2027 syllabus; numericals use only speed, distance and kinetic energy.

Practice questions on Centripetal Force: Sources and Work Done

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The work done by the centripetal force on a body in one complete revolution of radius $r$ is:
(a) $2 π r F$
(b) $F r$
(c) zero
(d) $2 F r$
Hint
Angle between force and displacement?
Answer
(c) zero
Q2 · 2 marks · Very short answerBoard level
Fill in the blanks: (a) The centripetal force is directed __________ the centre. (b) If the centripetal force stops, the body moves along the __________.
Hint
Centre-seeking; straight-line path.
Answer
(a) towards (b) tangent
Q3 · 2 marks · Short answerHarder board level
The Earth has kept going round the Sun for billions of years without any engine. Explain why no energy supply is needed to keep its speed.
Hint
Which force acts, and in which direction relative to the motion?
Answer
The Sun's gravitational pull provides the centripetal force, directed towards the Sun at right angles to the Earth's motion. It does no work, so the Earth's kinetic energy and speed are unchanged.
Q4 · 2 marks · Short answerHarder board level
A 1.5 kg ball tied to a string moves in a horizontal circle at a constant 4 m/s. Find (a) its kinetic energy, (b) the work done by the tension in 5 s.
Hint
Tension is perpendicular to the motion.
Answer
(a) $\frac{1}{2} \times 1.5 \times 4^{2} = 12$ J. (b) Zero.
Q5 · 3 marks · Short answerHarder board level
A marble rolls round the inside of a circular ring lying flat on a table. The ring has a small gap. Describe and draw the path of the marble after it reaches the gap. What provided its centripetal force before?
Hint
What pushed it inwards?
Answer
Before the gap, the push of the ring's wall (towards the centre) provided the centripetal force. At the gap this push stops, so the marble rolls off in a straight line along the tangent at the gap, not outwards along the radius.
Q6 · 2 marks · Short answerHarder board level
State whether a larger or a smaller centripetal force is needed in each case, for the same body: (a) it goes round the same circle faster, (b) it goes round a smaller circle at the same speed.
Hint
Think of a car taking bends.
Answer
(a) Larger. (b) Larger.
Q7 · 3 marks · Short answerHOTS / competency
A bead slides at constant speed round a smooth circular wire hoop lying flat on a table, making 3 rounds. (a) What provides its centripetal force? (b) How much work does this force do in the 3 rounds? (c) The wire is cut just ahead of the bead. What does the bead do?
Hint
The wire can push only sideways on the bead.
Answer
(a) The inward push of the wire on the bead. (b) Zero: the push is perpendicular to the motion at every instant. (c) It leaves the hoop and moves in a straight line along the tangent at the cut.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What provides the centripetal force for the Moon?Show answer
The Earth's gravitational pull.
2.Work done by the centripetal force in 5 rounds?Show answer
Zero.
3.Direction of motion just after a whirling string breaks?Show answer
Along the tangent at that point.
4.KE of a 1 kg body in uniform circular motion at 2 m/s?Show answer
2 J, and it stays constant.
5.Is the centripetal force real or apparent?Show answer
Real: it is supplied by an agent such as tension, gravity or friction.

Centripetal Force: Sources and Work Done: frequently asked questions

What is centripetal force in simple words?

It is the inward pull or push, towards the centre of the circle, that a body needs in order to keep moving in a circle instead of a straight line.

Why is the work done by centripetal force zero?

Because the force is along the radius and the motion is along the tangent, at right angles at every instant, so W = Fs cos 90° = 0.

Is centripetal force a separate kind of force?

No. It is the role played by a real force such as tension, gravity, friction or electrostatic attraction when that force keeps a body moving in a circle.