# Asimov pendulum

1. Apr 19, 2014

### alejandrito29

The aceleration in spherical coordinates is

$\vec{a} =( R \dot{\theta}^2 - R \omega^2 \sin ^2 \theta) \hat{r} + (R \ddot{\theta} - R \omega ^2 \sin \theta \cos \theta ) \hat{\theta} + (2R \dot{\theta} \omega \cos \theta) \hat{\phi}$

The forze is:

$-mg\hat{y}= -mg\cos(\frac{\pi}{2}-\theta) \hat{\theta} =-mg\sin(\theta) \hat{\theta}$

If i analize the theta component i find the answer for the equation of motion

$R \ddot{\theta} - R \omega ^2 \sin \theta \cos \theta = -g\sin(\theta)$

But, what happen with the other component of equation of motion?, why this does not appear in the books?

$R \dot{\theta}^2 - R \omega^2 \sin ^2 \theta =0$
$2R \dot{\theta} \omega \cos \theta=0$
In the last equation neither of the terms are zero.

Pd: I does not want to use the Lagran

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2. Apr 20, 2014

### Simon Bridge

Try solving the equation and find out.