What is the angular velocity of the drill bit in radians per second?

[Precursor]

Homework Statement

This problem is for a cordless drill.

[PLAIN]http://img718.imageshack.us/img718/8531/drill1.jpg

Homework Equations

[PLAIN]http://img442.imageshack.us/img442/3511/drill2.jpg

where N denotes number of teeth
w denotes angular velocity

The Attempt at a Solution

This is the work I have done so far:

$$\frac{9}{45} = \frac{x-720}{3600-x}$$

$$\frac{3600-x}{5} = x-720$$

$$x = \frac{5}{6}(1440)$$

$$x = 1200 rpm$$

I don't think I have completed the problem. Could someone please varify my work and show me what to do next?

 

[Precursor]

Anyone?

 

[Astronuc]

It appears to be correct, so far. One used N_ring*w_ring = N_sun*w_sun to obtain w_ring?

One has to convert revolutions per minute to radians per minute or per second. How many radians in a revolution?