# Pendulum in non inertial frame

1. Nov 12, 2013

### Luke1121

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

2. Relevant equations
$a_c=\frac{v^2}{R}=\omega^2R$

3. 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

2. Nov 12, 2013

### GregoryS

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

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

3. Nov 12, 2013

### Luke1121

Ah ok, so:

$Tcos\theta=mg (1) Tsin\theta=m\omega^2R (2)$

doing (2)/(1) gives

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

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