How do I determine θ'' and tension in a speed-governing mechanism?

[EserRose]

Homework Statement

In the speed-governing mechanism m = 0.2 kg, L = 10cm, (rods AB have negligible mass), w = 500 rpm, θ = 40°,θ' = 0 . Determine θ'' at that instant and the tension in the rod.

Homework Equations

F=[ω][/2]r

The Attempt at a Solution

First, I calculated ω = 500 rpm * 2π /60 = 52.36 rad/s.
From the vertical components, I determined T*cosθ = mg
So T = 2.56 N
With this, I can calculate the horizontal component of T, but then I have a different ω for the balls and I'm confused. Should I use polar coordinates? If so, how should I start?

 

[haruspex]

F=[ω][/2]r

What is F here? If it's a force, the dimensions don't match.

then I have a different ω for the balls

How do you mean? Remember, this is not equilibrium.

 

[EserRose]

What is F here? If it's a force, the dimensions don't match.

Ooos I meant m*ω^2 *r

How do you mean? Remember, this is not equilibrium.

I see that, so I should find the net force then?

 

[haruspex]

so I should find the net force then?

Sort of.. depends whether you want to use the inertial frame + centripetal view or object frame + centrifugal view.
In the latter case it would be net force; in the former you might describe it as the excess acceleration.