How can I find the radius of curvature (aka radius of the "kissing circle") if I have the momentum, mass, and components of the force?

Question

anonymous · Answer

You will want to use the equation for centripetal force, namely that the Force $F$ is $$F=\frac{mv^2}{r}$$ where $m$ is the mass, $v$ the velocity, and $r$ is the radius of curvature.  But we dont know the velocity, but this can be calculated from the momentum which you do know, since momentum $p$ is given by 

$$p=mv$$
 So, you can calculate the velocity first, and then plug it into the formula above, or you can combine the force equation with the momentum equation to give $$F=\frac{p^2}{mr}$$
 and solve for r.