In which direction is the acceleration of an object moving in a circle at constant speed?

towards the centre of the circle. The resultant force is towards the centre.

The speed of an object in circular motion doubles, with the same radius. What happens to the centripetal force needed?

It becomes four times bigger. F = mv² ÷ r.

How much work does the centripetal force do in one complete circle?

none. The force is always at right angles to the motion.

A stone on a string is whirled in a circle, and the string snaps. Which way does the stone move at first?

along the tangent to the circle. With no centripetal force it carries on in a straight line.

Centripetal force and acceleration · Cambridge A Level Physics

In plain words

Whirl a ball on a string and it keeps trying to fly off in a straight line, while the string keeps pulling it back towards the centre. That inward pull is the centripetal force. The ball's speed doesn't change but its direction changes all the time, and a change of direction is an acceleration.

4 things to know

An object moving in a circle at constant speed is accelerating, because its velocity keeps changing direction. The acceleration is towards the centre: a = v² ÷ r = rω².
That needs a resultant force towards the centre, the centripetal force: F = mv² ÷ r = mrω².
The centripetal force is not an extra force. It is provided by something real: tension, friction, gravity, a contact force, or a combination of them.
It is always at right angles to the motion, so it does no work and the speed stays the same.

Worked example

A 1200 kg car goes round a bend of radius 50 m at 15 m/s. Find the centripetal force needed, and say what provides it.

F = mv² ÷ r = 1200 × 15² ÷ 50.
= 5400 N.
It is provided by friction between the tyres and the road, acting towards the centre of the bend.

Tips and tricks

Never draw "centripetal force" as an extra arrow on a force diagram. Name the real force that provides it.
At the top or bottom of a vertical circle, the weight and the other force together must add up to mv² ÷ r towards the centre.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Centripetal force and acceleration: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

In which direction is the acceleration of an object moving in a circle at constant speed?
- towards the centre of the circle (the answer)
- away from the centre
- along the direction of motion
- there is none
The resultant force is towards the centre.
The speed of an object in circular motion doubles, with the same radius. What happens to the centripetal force needed?
- It doubles.
- It becomes four times bigger. (the answer)
- It halves.
- It stays the same.
F = mv² ÷ r.
How much work does the centripetal force do in one complete circle?
- none (the answer)
- F × 2πr
- F × r
- F × πr²
The force is always at right angles to the motion.
A 1000 kg car goes round a bend of radius 100 m at 20 m/s. What centripetal force is needed?
- 200 N
- 2000 N
- 4000 N (the answer)
- 200 000 N
1000 × 20² ÷ 100.
A stone on a string is whirled in a circle, and the string snaps. Which way does the stone move at first?
- along the tangent to the circle (the answer)
- straight outwards from the centre
- straight in towards the centre
- on round the circle
With no centripetal force it carries on in a straight line.

5 questions

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Worksheet

4 questions, 10 marks. Write your answers on paper, then check them.

Centripetal force and acceleration

Cambridge International AS & A Level Physics 9702 · 10 marks · papermunch.org

Name ______________________________ Date ______________

Find the centripetal acceleration of an object moving at 4.0 m/s in a circle of radius 0.50 m.[2]
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32 m/s².
I got this one
A 0.20 kg ball on a string moves in a horizontal circle of radius 0.80 m at an angular speed of 5.0 rad/s. Find the centripetal force on it.[3]
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4.0 N. 0.20 × 0.80 × 5.0².
I got this one
A 60 kg passenger is in a car that goes over a hump-back bridge of radius 40 m at 10 m/s. Find the force from the seat on the passenger at the top.[3]
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440 N. Towards the centre is downwards: mg − R = mv² ÷ r, so R = 589 − 150 N.
I got this one
Explain why an object moving in a circle at constant speed is accelerating.[2]
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Its direction of motion keeps changing, so its velocity is changing even though its speed is not. A changing velocity is an acceleration.
I got this one

Answers: Centripetal force and acceleration

1. 32 m/s².
2. 4.0 N. 0.20 × 0.80 × 5.0².
3. 440 N. Towards the centre is downwards: mg − R = mv² ÷ r, so R = 589 − 150 N.
4. Its direction of motion keeps changing, so its velocity is changing even though its speed is not. A changing velocity is an acceleration.