Centripetal acceleration: derivation of a= v2/r

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SUMMARY

The formula for centripetal acceleration, expressed as a = v²/r, is derived by analyzing the motion of a particle subjected to a sideways force. When a particle travels with speed v through a small angle Δθ, the change in velocity Δv can be represented as Δv = vΔθ. The acceleration a is then defined as a = Δv/Δt, which can be rewritten using the relationship Δt = rΔθ/v, leading to the final expression for centripetal acceleration.

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  • Study the relationship between linear and angular velocity in circular motion.
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Lindsey
Can anyone please tell me how the formula for centripetal acceleration (a=v2/r) is derived?
 
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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 traveled while the force is being applied is

vΔt=rΔθ

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

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