Question

Centrifugal force derivation

Answer 1

The force of a moving body is given as

F = ma........(1)


From the figure, we can write the expression

= PQ→PQ→ + QS→QS→ = PS→PS→

= -v1v1 + v2v2
= ΔvΔv

= ΔvΔv = v2v2 - v1v1

The triangle AOB and PQS are similar. So

= ΔvABΔvAB = vrvr

AB = arc  
AB = vΔΔ t

= ΔvvΔtΔvvΔt = vrvr

= ΔvΔtΔvΔt = v2rv2r

= a = v2rv2r

Substitute this value in (1) we get the centripetal force

therefore......
F = mv2rv2r = mrω2


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