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A LevelPhysicsCIERevision Notes12. Motion in a Circle12.2 Centripetal AccelerationCalculating Centripetal Acceleration

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First exams 2025

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Calculating Centripetal Acceleration (CIE A Level Physics)

Revision Note

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Leander

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Calculating centripetal acceleration

  • Centripetal acceleration is defined as:

The acceleration of an object towards the centre of a circle when an object is in motion (rotating) around a circle at a constant speed

  • It can be defined using the radius r and linear speed v:

a space equals fraction numerator space v squared over denominator r end fraction

  • Where:
    • a = centripetal acceleration (m s–2)
    • v = linear speed (m s–1)
    • r = radius of the circular orbit (m)
  • Using the equation relating angular speed ω and linear speed v:

v space equals space r omega

  • Where:
    • ω = angular speed (rad s–1)

  • These equations can be combined to give another form of the centripetal acceleration equation:

a space equals fraction numerator space open parentheses r omega close parentheses squared over denominator r end fraction

a space equals space r omega squared

Centripetal acceleration

Centripetal acceleration diagram, downloadable AS & A Level Physics revision notes

Centripetal acceleration is always directed toward the centre of the circle, and is perpendicular to the object’s velocity

 

  • Where:
    • a = centripetal acceleration (m s−2)
    • v = linear speed (m s−1)
    • ⍵ = angular speed (rad s−1)
    • r = radius of the orbit (m)

Worked example

A ball tied to a string is rotating in a horizontal circle with a radius of 1.5 m and an angular speed of 3.5 rad s−1.

Calculate its centripetal acceleration if the radius was twice as large and angular speed was twice as fast.

Answer:

Step 1: State acceleration in terms of angular speed

a space equals space r omega squared

Step 2: Increase angular acceleration with twice the radius and twice the angular speed

a space equals space open parentheses 2 r close parentheses space cross times space open parentheses 2 omega close parentheses squared space equals space 2 r space cross times space 4 space omega squared space equals space 8 r omega squared

  • The centripetal acceleration will be 8× bigger

Step 3: Substitute in the known values to calculate

a space equals space 8 r omega squared space equals space 8 space cross times space 1.5 space cross times space 3.5 squared space equals space 147 space straight m space straight s to the power of negative 2 end exponent

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    Leander

    Author: Leander

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.