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

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First teaching 2023

First exams 2025

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Calculating Centripetal Force (CIE A Level Physics)

Revision Note

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Calculating centripetal force

  • Centripetal force can be calculated using the equations:
    • Centripetal force and linear velocity, v

F space equals fraction numerator space m v squared over denominator r end fraction

    • Centripetal force and angular velocity, ω

F space equals space m v omega

  • Where:
    • F = magnitude of the centripetal force, measured in newtons (N)
    • m = mass of object, measured in kilograms (kg)
    • v = velocity, measured in meters per second (m s-1)
    • r = radius of orbit, measured in meters (m)
    • omega = angular velocity measured in radians per second (rad s-1)
  • These two equations for centripetal force are equivalent because of the equation linking linear and angular velocity

v space equals space r omega

    • Substituting into the first centripetal force equation

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

    • Simplify the equation

F space equals space fraction numerator m r squared omega squared over denominator r end fraction space equals space fraction numerator m r to the power of up diagonal strike 2 end exponent omega squared over denominator up diagonal strike r end fraction space equals space m r omega squared

Centripetal force

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

Centripetal force is always perpendicular to the direction of travel

Worked example

A bucket of mass 8.0 kg is filled with water is attached to a string of length 0.5 m.

What is the minimum speed the bucket must have at the top of the circle so no water spills out?

WE - Centripetal force question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Draw the forces on the bucket at the top

Step 2: Calculate the centripetal force

  • The weight of the bucket = mg
  • This is equal to the centripetal force since it is directed towards the centre of the circle

m g space equals fraction numerator space m v squared over denominator r end fraction

Step 3: Rearrange for velocity v

  • m cancels from both sides

v space equals space square root of g r end root

Step 4: Substitute in values

v space equals space square root of 9.81 space cross times space 0.5 end root space equals space 2.21 space straight m space straight s to the power of negative 1 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.