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## Homework Statement

Basically i have to prove a lagrange equation using a non-inertial reference frame. A bead on a hoop where the hoop rotates as in the image below.

F = F

_{g}+ F

_{cf}

## Homework Equations

mR(d

^{2}θ/dt

^{2}) = mΩ

^{2}Rcosθsinθ -mgsinθ

what I'm supposed to get

## The Attempt at a Solution

F

_{g}= -mgsinθ

F

_{cf}= m(ΩxR)xΩ = mΩ

^{2}Rcosθsinθ

I know that

Ω = Ω(0 , sinθ, cosθ)

R = R( 0 , k I'm just lost and frustrated :(