Pendulum in non inertial frame

[Luke1121]

Homework Statement

A pendulum is placed on a rotating platform which rotates with angular velocity ω around an axis, at equilibrium the angle between vertical and pendulum is θ
θ= 20 degrees
ω= 10 1/s
how far is the pendulum placed from the axis

Homework Equations

[itex]a_c=\frac{v^2}{R}=\omega^2R[/itex]

The Attempt at a Solution

the frame is non inertial so effective g is [itex]\sqrt{g^2 + \omega^2R}[/itex]

I'm not really sure where to go from here, i thought about doing
[itex] \omega=\sqrt{\frac{g}{l}}=\sqrt{\frac{g^2 + \omega^2R}{l}}[/itex] and solving for R however [itex]l[/itex] isn't given so I'm not really sure where to go next, any ideas?

Thanks, Luke

 

[GregoryS]

You are wrong considering a mathematical pendulum instead of conic one.

So you may write down (T is a funicular force):
$$
m a_c = m ω^2 R = T sinθ
$$
$$
0 = T cosθ - m g
$$

 

[Luke1121]

You are wrong considering a mathematical pendulum instead of conic one.

So you may write down (T is a funicular force):
$$
m a_c = m ω^2 R = T sinθ
$$
$$
0 = T cosθ - m g
$$

Ah ok, so:

[itex]Tcos\theta=mg (1)
Tsin\theta=m\omega^2R (2) [/itex]


doing (2)/(1) gives

[itex]R=\frac{gtan\theta}{\omega^2}[/itex]

plugging in the numbers gives 0.036m, is this correct?