Centripetal acceleration: derivation of a= v2/r

  • Thread starter Lindsey
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  • #1
Can anyone please tell me how the formula for centripetal acceleration (a=v2/r) is derived?
 

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  • #2
Ambitwistor
841
1
Google will give you many derivations, some with pictures; for instance:

http://www.usafa.af.mil/dfp/cockpit-phys/pg1th31.htm
http://www-istp.gsfc.nasa.gov/stargaze/Scircul.htm
http://home.cc.umanitoba.ca/~loly/rotator.pdf
http://www.pa.uky.edu/~moshe/phy231/lecture_notes/circular.html
 
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  • #3
krab
Science Advisor
893
3
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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