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Centripetal acceleration: derivation of a= v2/r

  1. Nov 14, 2003 #1
    Can anyone please tell me how the formula for centripetal acceleration (a=v2/r) is derived?
     
  2. jcsd
  3. Nov 14, 2003 #2
  4. Nov 14, 2003 #3

    krab

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    Science Advisor

    Let's say a sideways force deflects a particle traveling with speed v through a small angle Δθ. Then Δv=vΔθ, and the acceleration is

    a=Δv/Δt=vΔθ/Δt

    The distance travelled while the force is being applied is

    vΔt=rΔθ

    Solve the second displayed equation for Δt and plug it into the first equation. There ya go.
     
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