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First teaching 2014

Last exams 2024

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Centripetal Force (DP IB Physics: SL)

Revision Note

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David Lancefield

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Centripetal Force

  • An object moving in a circle is not in equilibrium, it has a resultant force acting upon it
    • This is known as the centripetal force and is what keeps the object moving in a circle

  • The centripetal force (F) is defined as:

The resultant force perpendicular to the velocity, and therefore directed towards the centre of the circle, required to keep a body in uniform circular motion

  •  The magnitude of the centripetal force F can be calculated using:

Calculating Centripetal Force equation 1

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

Centripetal force is always perpendicular to the linear velocity (i.e., the direction of travel)

  • Where:
    • F = centripetal force (N)
    • v = linear speed (m s1)
    • ⍵ = angular speed (rad s−1)
    • r = radius of the orbit (m)

  • Note: centripetal force and centripetal acceleration act in the same direction
    • This is due to Newton's Second Law

  • The centripetal force is not a separate force of its own
  • It can be any type of force, depending on the situation, which keeps an object moving in a circular path
    • For example, tension, friction, gravitational, electrical or magnetic

Examples of centripetal forceTable showing examples of centripetal force, downloadable AS & A Level Physics revision notes

  • When solving circular motion problems involving one of these forces, the equation for centripetal force can be equated to the relevant force equation
  • For example, for a charged particle travelling in a circle, the centripetal force causing the charged particle to move in a circle is provided by the magnetic force
  • Therefore, equating the expressions for centripetal force and magnetic force gives the following:

Centripetal & Magnetic Force Equation_2

  • Where:
    • B = magnetic field strength (T)
    • q = charge on the particle (C)
    • m = mass of the particle (kg)
    • v = speed of the particle (m s−1)
    • r = radius of orbit (m)

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

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

Step 3: Rearrange for velocity v

    • m cancels from both sides

Step 4: Substitute in values

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