# Maximum angular velocity from a swing carousel

**2. Relevant equations**

At first, I thought this was easy where T = mgcosθ + mω^{2}rsinθ . But then I realised there were several problems with this firstly that we don’t know theta and so can’t work out ω when θ is also unknown. But also that using r is incorrect as the true radius that the passenger is revolving round is larger due to the centripetal force making them swing out.

I derived this formula for the necesarry condintions for the passenger being in equilibrium mgsinθ = mω^{2}cosθ(r + lcosθ) . However it doesn’t help me much at this stage. The problem is I know that θ and ω are dependant in that if I determine an angular velocity, I will get a corresponding value for θ when the system is in equilibrium.

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

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