Final answer:
The basis is rotated by an angle φ from the Cartesian coordinate system, which includes unit vectors i and ć. The polar coordinate system uses radial unit vector F and an orthogonal vector t for describing point positions in the plane.
Step-by-step explanation:
The basis is rotated by an angle φ from the Cartesian basis. The Cartesian coordinate system uses unit vectors i and ć along the x-axis and y-axis respectively, which provide two orthogonal directions in the plane. However, for describing rotations or circular motion, it becomes more convenient to use the polar coordinate system. This system employs a radial unit vector F, which points directly away from the origin, and an orthogonal unit vector t, which is perpendicular to F. In this sense, vector F aligns with the radial coordinate (distance from the origin), while vector t defines the positive direction of rotation by the angle φ.
In summary, when converting from the Cartesian system to the polar coordinate system, unit vectors are rotated to align with the radial and angular directions, characterized by F and t vectors respectively.