OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Centripetal force: (c) centripetal acceleration; a = v²/r; a = ω²r
Centripetal acceleration is the acceleration of a body moving in a circle at constant speed.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Centripetal acceleration is the acceleration of a body moving in a circle at constant speed. Because velocity is a vector, its direction changes continuously, so the body accelerates even though its speed is constant. This acceleration acts towards the centre of the circle, perpendicular to the instantaneous velocity. For a body moving at speed v on a circle of radius r, the magnitude is a = v²/r. Since v = ωr, substituting gives a = (ωr)²/r = ω²r, so a = ω²r. For example, a ball whirled on a 0.50 m string at 4.0 m s⁻¹ has a = (4.0)²/0.50 = 32 m s⁻², directed towards the centre. Angular speed ω is measured in rad s⁻¹, so ω²r gives m s⁻².
What earns the marks
- States that centripetal acceleration is directed towards the centre of the circular path, perpendicular to the instantaneous velocity.
- Uses a = v²/r correctly, substituting speed in m s⁻¹ and radius in m, to obtain acceleration in m s⁻².
- Uses a = ω²r correctly, with ω in rad s⁻¹ and r in m, to obtain acceleration in m s⁻².
- Explains that speed is constant but velocity changes direction, so the body accelerates.
- Links the two forms through v = ωr, showing a = v²/r and a = ω²r are equivalent.
Common mistakes and how to put them right
Thinking a body moving at constant speed in a circle has zero acceleration.
Put it right by noting velocity changes direction, so acceleration is non-zero and directed towards the centre.
Treating centripetal acceleration as directed outwards or along the tangent.
Put it right by stating it always points towards the centre, perpendicular to velocity.
Using diameter in place of radius in a = v²/r.
Put it right by halving any diameter before substituting.
Mixing units by using ω in degrees per second or revolutions per minute.
Put it right by converting to rad s⁻¹ before using a = ω²r.
Exam tips
- Check whether the question gives v or ω, then choose a = v²/r or a = ω²r to avoid an unnecessary conversion step.
- Convert any angular speed in rev min⁻¹ to rad s⁻¹ by multiplying by 2π and dividing by 60 before substituting.
- State the direction of the acceleration as towards the centre whenever the question asks for a vector quantity.
Try the lesson
The start of the Centripetal force: (c) centripetal acceleration; a = v²/r; a = ω²r lesson, made from checked teaching notes for this specification point.
Listen
Centripetal acceleration is the acceleration of a body moving in a circle at constant speed. Because velocity is a vector, its direction changes continuously, so the body accelerates even though its speed is constant. This acceleration acts towards the centre of the circle, perpendicular to the instantaneous velocity. For a body moving at speed v on a circle of radius r, the magnitude is a = v²/r. Since v = ωr, substituting gives a = (ωr)²/r = ω²r, so a = ω²r. For example, a ball whirled on a 0.50 m string at 4.0 m s⁻¹ has a = (4.0)²/0.50 = 32 m s⁻², directed towards the centre. Angular speed ω is measured in rad s⁻¹, so ω²r gives m s⁻². A strong answer earns marks for these points. States that centripetal acceleration is directed towards the centre of the circular path, perpendicular to the instantaneous velocity. Uses a = v²/r correctly, substituting speed in m s⁻¹ and radius in m, to obtain acceleration in m s⁻². Uses a = ω²r correctly, with ω in rad s⁻¹ and r in m, to obtain acceleration in m s⁻². Explains that speed is constant but velocity changes direction, so the body accelerates. A common slip: Thinking a body moving at constant speed in a circle has zero acceleration. Instead, noting velocity changes direction, so acceleration is non-zero and directed towards the centre. Exam tip: Check whether the question gives v or ω, then choose a = v²/r or a = ω²r to avoid an unnecessary conversion step.
Key words
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Centripetal acceleration
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Vector nature of velocity and acceleration
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Centripetal acceleration magnitude and direction
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Relationship between linear and angular speed
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See every definition
- Centripetal acceleration
- The acceleration of a body moving in a circle at constant speed, acting towards the centre of the circle and perpendicular to the instantaneous velocity.
- Vector nature of velocity and acceleration
- Because velocity is a vector, its direction changes continuously, so the body accelerates even though its speed is constant.
- Centripetal acceleration magnitude and direction
- For a body moving at speed v on a circle of radius r the magnitude is a = v²/r, directed towards the centre.
- Relationship between linear and angular speed
- Since v = ωr, substituting gives a = (ωr)²/r = ω²r, so a = ω²r.
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