I am not sure where this problem belongs, but it was proposed by my math teacher as a challenge. Problem: An ant is located on a bowl that has the shape of a semi sphere and he is just able to get out of the bowl. The coefficient of static friction between the ant and the bowl is 1/3. Find the radius of the bowl. My attempt: Mu is the tangent ratio between Friction and Normal forces. The angle that is found by taking the arctangent(1/3) is also the angle that the radius is currently making with from the 0 position(bottom of the bowl). Since this is a bowl, the line tangent to the circle would be the slope used to calculate friction. Therefore as the line changes so does Mu, as of course is the angle. There is no time interval give. Since we are given a specific angle and nothing else relating to the bowl itself (my assumption) I decided to put this problem in polar coordinates. I represented the bowl as r=sin(?) and plugged in the angle. This produces a radius of (1/10)^(.5)meters. However, this seems like a forced solution to me. I thought about trying to find the position of the ant, but because the bowl could be located anywhere I couldn't treat this as a freefall problem. Thanks for your help.