Problem $1$

An acrobat weights $150$ lbf and is sitting on a chair atop a long pole. The pole is rotated at a constant angular speed so that the acrobat's center of mass G moves at a constant speed of $20f\frac{t}{s}.$ The coefficient of static friction between the person and the chair is $0\mathrm{.}35.$ Determine the angle $$ at which the acrobat begins to 'fly' out of the chair. Use $=15ft.$