Circular motion and static friction of earth

[brownie24]

Homework Statement

A platform on Earth rotates at constant angular speed 2 rad/s. A 60 kg man stands on the platform. Static friction between the platform and the man's feet prevent slipping.
(a) Make a diagram showing the forces he exerts on the platform standing a distance r from the axis of rotation. r = 0, 1, 2
(b) What direction does the man sense as "up"? Calculate the angle that "up" makes with the vertical using values of r as stated.
(c) If plants were planted on the platform, in what direction would they grow?

Homework Equations

a = omega^2 r

The Attempt at a Solution

(a) In the x plane, force of friction acts as force of centripetal acceleration = m omega^2 r. What I don't understand is what is the reactive force?
In the y plane, normal force opposes gravitational force = mg. If this is so, the man's weight should be constant, despite his distance from the rotational axis. Is (a) a trick question?

 

[Hootenanny]

Welcome to Physics Forums.

(a) In the x plane, force of friction acts as force of centripetal acceleration = m omega^2 r. What I don't understand is what is the reactive force?

It doesn't matter what we call the reaction force merely that one exists. Since the table exerts a force on the man, the man must also exert a force on the table in the opposite direction (i.e. radially outward) and of the same magnitude. I am being intentionally vague regarding the 'name' of this reaction force to avoid a long discussion on the centrifugal force.

In the y plane, normal force opposes gravitational force = mg. If this is so, the man's weight should be constant, despite his distance from the rotational axis. Is (a) a trick question?

No trick, you are indeed correct.

 

[nlightner]

(b) The man would sense "up" as the direction opposite to the centripetal force, which would be pointing towards the center of the circle. The angle that "up" makes with the vertical would be 90 degrees, regardless of the value of r. This is because the force of gravity and the normal force are always acting perpendicular to the surface of the platform, and thus the direction of "up" is always perpendicular to the surface as well.

(c) If plants were planted on the platform, they would grow in the direction of the normal force, which is always perpendicular to the surface of the platform. So regardless of the value of r, the plants would grow straight towards the center of the circle, towards the axis of rotation.