In an exhibit at the NASA museum in Huntsville, AL, there is a “human centrifuge”. Guests

Question

stand upright against the walls of a circular room with a radius of 8 meters which then spins
at an angular velocity ω about an axis through its center. Then, once the room is spinning,
the floor drops away from the guests’ feet. They feel themselves pressed against the walls,
but do not fall.

a) Draw a force diagram for the person in this exhibit. Make sure you label the axes in your
force diagram to indicate which direction is “up”, and which direction points toward the
center of the circular room.
b) Suppose the coefficient of static friction between the guests’ clothing and the wall is 0.4.
At what angular velocity ω must the room spin to ensure that the guests do not fall?
c) Guests in this exhibit feel themselves “pressed against the walls”, and find it very difficult
to lift their arms away from the wall; for instance, it may require a force of 25 N to hold
a one-kilogram object in place away from the wall. Is there a force pressing the guests and
their hands against the wall? If so, what is that force? If not, how do you explain the
difficulty lifting objects away from the wall?