Universal Gravitation and neutron stars

[1st2fall]

Homework Statement

Certain neutron stars (extremely dense stars) are believed to be rotating at about 6 rev/s. If such a star has a radius of 15 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?


G=6.67*10^-11m³ kg^-1 s^-2

Homework Equations

$$F_c{}=\frac{mv^{2}}{r}$$
$$F_g{}=\frac{GM_1{M_2{}}}{r^{2}}$$

The Attempt at a Solution

30$$\pi$$km*6rev/s=180$$\pi$$km/s
which gives the linear velocity of something on the surface of the neutron star... but I'm clueless as to how to arrive at a mass of the star from it. I could the Centripetal acceleration but I'm not sure how that's related here. the only thing I can think of there is setting the centripetal acceleration equal to the gravitation acceleration which gives

Gm/r²=v²/r
m=v²r/G
which yields something like 7.28635682 × 10^24(kg?)

I'm just looking for advice on what I'm actually looking to do. I don't know what I should be looking for...

 

[ehild]

Your formula is correct, but check the calculation.

ehild

 

[1st2fall]

Thank you very much! I realized a dropped a "pi" at some point when I went back over it.