AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Motion in a circular path at constant speed implies there is an…
Full specification wording
Circular motion (A-level only): Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force.
An object moving in a circle at constant speed still accelerates because its velocity changes direction continuously.
Checked against the AQA 7408 specification (opens in a new tab) on .
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
An object moving in a circle at constant speed still accelerates because its velocity changes direction continuously. The acceleration is directed towards the centre of the circle and has magnitude a = v²/r, where v is the speed and r is the radius. By Newton's second law, a resultant force called the centripetal force acts towards the centre, with magnitude F = mv²/r. The force is not a new type of force; it is provided by tension, gravity, friction, normal contact force or a combination. For example, a ball whirled on a string has tension as the centripetal force, while a satellite in orbit has gravitational force. If the centripetal force is removed, the object moves in a straight line tangent to the circle.
What earns the marks
- State that velocity is a vector, so changing direction at constant speed changes velocity and therefore produces acceleration.
- Identify the direction of the centripetal acceleration as towards the centre of the circular path.
- Use a = v²/r to calculate centripetal acceleration when speed and radius are known.
- Apply Newton's second law in the form F = mv²/r to find the resultant centripetal force.
- Recognise that the centripetal force is provided by an existing force such as tension, friction, gravity or normal contact force, not an extra force.
- Explain that removing the centripetal force makes the object move along the tangent to the circle at that instant.
Common mistakes and how to put them right
Thinking that constant speed means zero acceleration.
Put it right by noting that velocity changes direction, so acceleration is non-zero and directed towards the centre.
Adding a separate outward centrifugal force to force diagrams.
Put it right by showing only the real inward resultant force that provides the centripetal acceleration.
Using a = v²/r with diameter instead of radius.
Put it right by using the radius, which is half the diameter.
Exam tips
- Draw a clear free-body diagram showing the resultant force directed towards the centre and label the force that provides it.
- Show the substitution into a = v²/r or F = mv²/r with consistent units before calculating.
- When explaining motion, refer to the change in direction of velocity rather than a change in speed.
Try the lesson
The start of the Circular motion (A-level only): Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force. lesson, made from checked teaching notes for this specification point.
Have a go first
An object moves in a circular path at constant speed. Why does this motion involve an acceleration?
Listen
An object moving in a circle at constant speed still accelerates because its velocity changes direction continuously. The acceleration is directed towards the centre of the circle and has magnitude a = v²/r, where v is the speed and r is the radius. By Newton's second law, a resultant force called the centripetal force acts towards the centre, with magnitude F = mv²/r. The force is not a new type of force; it is provided by tension, gravity, friction, normal contact force or a combination. For example, a ball whirled on a string has tension as the centripetal force, while a satellite in orbit has gravitational force. If the centripetal force is removed, the object moves in a straight line tangent to the circle. A strong answer earns marks for these points. State that velocity is a vector, so changing direction at constant speed changes velocity and therefore produces acceleration. Identify the direction of the centripetal acceleration as towards the centre of the circular path. Use a = v²/r to calculate centripetal acceleration when speed and radius are known. Apply Newton's second law in the form F = mv²/r to find the resultant centripetal force. A common slip: Thinking that constant speed means zero acceleration. Instead, noting that velocity changes direction, so acceleration is non-zero and directed towards the centre. Exam tip: Draw a clear free-body diagram showing the resultant force directed towards the centre and label the force that provides it.
Key words
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Centripetal acceleration
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Centripetal force
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Vector nature of velocity and acceleration
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Tangential motion when force is removed
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See every definition
- Centripetal acceleration
- Directed towards the centre of the circle and has magnitude a = v²/r, where v is the speed and r is the radius.
- Centripetal force
- A resultant force acting towards the centre, with magnitude F = mv²/r, required by Newton's second law.
- Vector nature of velocity and acceleration
- Velocity is a vector, so changing direction at constant speed changes velocity and therefore produces acceleration.
- Tangential motion when force is removed
- If the centripetal force is removed, the object moves in a straight line tangent to the circle.
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