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## Homework Statement

Consider the bead threaded on a cicular hoop of example 7.6 (pg 260), working in a frame that rotates with the hoop. find the equation of motion of the bead, and check that your result agrees with eq 7. 69. Using a free body diagram explain the result 7.71 for equilibrium positions

## Homework Equations

d

^{2}θ/dt

^{2}= (ω

^{2}cosθ - g/R)sinθ 7.69

θ

_{o}= ±arccos(g/ω

^{2}R) 7.72

## The Attempt at a Solution

In the inertial frame there is going to be a centrifugal force coriolus force and force of gravity

F

_{eff}= F

_{g}+ F

_{cf}+ F

_{cor}

by the diagram

F

_{cf}= mRω

^{2}sinθ Not sure about the direction

( I'm thinking it wouldn't really be in the r hat direction. more like Rcosθ. sounds redundant but i'm not sure how to explain it.)

F

_{cor}= -2mvΩcosθ because it is in the southern hemisphere so it would deflect left which would oppose the gravitational force

I assume F

_{eff}= mR

^{2}[d

^{2}θ/dt

^{2}]

I can solve this problem by lagrange method, but i'm not fully understanding this non-inertial ref frame.