A particle of mass m slides smoothly on the inside of a cone that has a vertical axis and has a semi-angle of 7/4, as shown in the figure below. Let (r, ø, z) be cylindrical polar coordinates, with the origin at the vertex of the cone. Suppose z and o are chosen as generalised coordinates for the particle. Determine the kinetic energy of the particle in terms of these generalised coordinates.

A particle of mass m slides smoothly on the inside of a cone that has a vertical axis and has a semi-angle of 7/4, as shown in the figure below. Let (r, ø, z) be cylindrical polar coordinates, with the origin at the vertex of the cone. Suppose z and o are chosen as generalised coordinates for the particle. Determine the kinetic energy of the particle in terms of these generalised coordinates.