Asurface charge density σ(θ)=σ0cosθ is glued to the surface of a spherical shell of radius r (σ0 is a constant and θ is the polar angle). there is a vacuum, with no charges, both inside and outside of the shell. calculate the electrostatic potential and the electric field both inside and outside of the spherical shell.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm