P1(10pts). A classic model for artificial gravity in a space-station is to have a rotating habitat that spins around a central axis with constant angular frequency w as shown in the figure below. The ring of the space station has a radius of R = 20m. Ignore gravitational forces. Answer the following: W a. Draw a FBD for an astronaut standing on the inside of the ring of the habitat. b. What must be the rotation rate (in rad/s) of the space-station for the normal force against the astronaut to be equivalent to the normal force (mg) on earth? c. If a ring with a circumference of 300km was to have the same normal force as (b), what is the period of rotation? d. Treat the habitat as a thin ring of mass, if the station reaches the rotational rate from part (b) in 50.0s after a torque of 2000 Nm is applied, what must the mass of the station be