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Centripetal forces review

Review the key concepts, equations, and skills for centripetal forces, including that centripetal force is the net force in the radial direction.

Key terms

Term (symbol)Meaning
Centripetal force (Fc)Net force acting in the direction towards the center of a circular path, causing centripetal acceleration. Direction is perpendicular to the object’s linear velocity. Also sometimes called radial force.

Equations

EquationSymbol breakdownMeaning in words
ΣFR=macac is centripetal acceleration, m is mass, and ΣFR is net force in radial direction (or centripetal force)Net radial force is directly proportional to the product of the object's mass and centripetal acceleration.

Common mistakes and misconceptions

  • Centripetal force is not a type of force. Centripetal force is a net force is the sum of the force vectors pointing in the radial direction. It could be the component of a force, the sum of multiple forces, or the difference of two radial vectors.
  • People mistakenly think objects moving in a circular path are acted upon by an outwards pointing force. When you turn in a circle, it may feel like something is pulling you outwards from the turn, but that’s your inertia trying to resist a change in motion.

Learn more

For deeper explanations of centripetal force, see our video introducing centripetal force using flaming test balls.
To check your understanding and work toward mastering these concepts, check out the exercise on centripetal forces.

Want to join the conversation?

  • blobby green style avatar for user Amy Wang
    ΣF r is net force in radial direction, then it could be the difference of two radial vectors that are pointing in opposite directions? (such as the difference between force of tension and gravitational force) Also, I noticed how the object attached to a string wouldn't actually rotate unless you exert a force that could spin up the string, so it there a notion to explain this? thank you!
    (12 votes)
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    • mr pink red style avatar for user Kavya Rathi
      Yes, you are correct. The net force in the radial direction (ΣFᵣ) can indeed be the difference of two radial vectors pointing in opposite directions, like the difference between the force of tension and gravitational force. When these forces are in balance, the object experiences no radial acceleration.

      Regarding the object attached to a string not rotating unless you exert a force to spin up the string, this is related to the concept of centripetal force. When an object is moving in a circular path, there must be a force acting towards the center of the circle (centripetal force) to keep it in that circular motion. Without this inward force, the object would move in a straight line due to its inertia. So, in the case of an object attached to a string, if you don't apply enough force to overcome its inertia and provide the necessary centripetal force, it won't rotate and will simply move in a straight line.
      (2 votes)
  • blobby green style avatar for user Cassie Geraghty
    In the roller coaster example, because more forces are added onto the centrifugal force, that means that the centrifugal force gets larger, correct?
    (4 votes)
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    • blobby green style avatar for user A P
      Yes. Remember that the centripetal force is not a type of force in itself (like forces of gravity, tension, or the normal force), but instead just a name we give to any force causing the object to undergo circular motion.
      (4 votes)
  • blobby green style avatar for user subject0477
    If physics over complicates things one more time, I'm going back in time and fighting Issac Newton >:(
    (4 votes)
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  • stelly green style avatar for user Perla Guzman
    noticed how the object attached to a string wouldn't actually rotate unless you exert a force that could spin up the string, so it there a notion to explain this?
    (3 votes)
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  • blobby green style avatar for user odiaseemwinghama
    Is centripetal force a vector quantity
    (1 vote)
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    • female robot grace style avatar for user Sukhada
      Since v and R are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, centripetal acceleration is not a constant vector.
      (1 vote)
  • blobby green style avatar for user shyakaprince56
    how can you find the centripetal acceleration when you are given the length of the string and mass and v only?
    (1 vote)
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