Near the Earth's surface, a compact car of total mass M is driven on a large, revolving, horizontal, disk-shaped platform which itself rotates about its center at a fixed angular frequency ω. At t = 0, the driver leaves the origin and drives outward along a line painted radially on the platform. The driver attempts to maintain a constant speed v_0 relative to the surface of the disk. Ignore the rotation of the earth and any air resistance but assume friction between the car and the disk, characterized by a coefficient of friction μ. Take the Earth to be an inertial frame.
(a) Use cylindrical coordinates to express the acceleration of the car as a function of time t (in the frame of the Earth).