Finding angular velocity for a rope to be cut

[Like Tony Stark]

Homework Statement

The bodies shown in the picture spin on a horizontal plane, describing a circular path with constant acceleration. They're connected by ropes that resist $1100 N$ (each rope). Find the angular velocity when one of the ropes is cut.

Relevant Equations

Newton's equation

I wrote Newton's equations for each body (I took $x$ as the axis aligned with the tension)

$m_1$:
$x)f*_1 -T_1+T_2=0$
Where $f*_1=\omega ^2 r_1$

$m_2$
$x)f*_2 -T_2=0$
$x)f*_2=T_2$
Where $f*_2=\omega ^2 r_2$

I wrote that $T_2=1100 N$ and solved for $\omega$, and I got $\omega =20.56 \frac{rad}{s}$.

Then, I wrote $T_2=f*_2$ in the equation for $m_1$, replace $T_1=1100$ and solved for $\omega$. Doing so I found that $\omega = 16.37 \frac{rad}{s}$.

So, the first rope will be cut with less angular velocity.

Is this right?

 

[TSny]

This looks good to me. But note that your first equation (for $m_1$) shows that $T_1$ is going to be greater than $T_2$ for any value of $\omega$ up until one of the ropes breaks.