# Centripetal acceleration: derivation of a= v2/r

Can anyone please tell me how the formula for centripetal acceleration (a=v2/r) is derived?

Ambitwistor
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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Let's say a sideways force deflects a particle traveling with speed v through a small angle &Delta;&theta;. Then &Delta;v=v&Delta;&theta;, and the acceleration is

a=&Delta;v/&Delta;t=v&Delta;&theta;/&Delta;t

The distance travelled while the force is being applied is

v&Delta;t=r&Delta;&theta;

Solve the second displayed equation for &Delta;t and plug it into the first equation. There ya go.