why would vectors being written in terms of polar co-ordinates? What advantage does it confer when studying circular motion?
while studying circular motion we are interested in radial and tangential forces. the radial and tangential directions change with time so if we use cartesian coordinates then we will have to bother ourselves with taking components along the radial and tangential directions. polar coordinates make it very natural. you directly get the forces along the tangential and the radial directions.