Centripetal acceleration: derivation of a= v2/r

L

Lindsey

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

krab

Science Advisor
896
1
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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