How Far is the Pendulum from the Axis on a Rotating Platform?

[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

a_c=\frac{v^2}{R}=\omega^2R

The Attempt at a Solution

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

I'm not really sure where to go from here, i thought about doing
\omega=\sqrt{\frac{g}{l}}=\sqrt{\frac{g^2 + \omega^2R}{l}} and solving for R however l 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:

Tcos\theta=mg (1)<br /> Tsin\theta=m\omega^2R (2)


doing (2)/(1) gives

R=\frac{gtan\theta}{\omega^2}

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