Circular motion and static friction of earth

In summary: The man's weight will not change regardless of his distance from the axis. However, the direction of the normal force will change as the man moves along the platform. And since the normal force is the reaction force to the man's weight, it will also change direction.In summary, a 60 kg man standing on a rotating platform with an angular speed of 2 rad/s will experience a force of friction and a normal force acting on him. The man's weight will remain constant regardless of his distance from the rotational axis, but the direction of the normal force and the reaction force will change. This is important to consider when determining the direction of "up" for the man and the direction in which plants would grow on the
  • #1
brownie24
3
0

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?
 
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  • #2
Welcome to Physics Forums.
brownie24 said:
(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.
brownie24 said:
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.
 
  • #3


(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.
 

Related to Circular motion and static friction of earth

1. What is circular motion and how does it relate to the Earth?

Circular motion is the movement of an object along a circular path. In the case of the Earth, it is constantly moving in a circular path around the sun, which is known as its orbit. This motion is controlled by the gravitational pull between the Earth and the sun.

2. How does static friction play a role in the Earth's circular motion?

Static friction is the force that prevents two surfaces from sliding against each other when there is no relative motion between them. In the case of the Earth, static friction between the Earth's surface and the atmosphere helps to maintain the circular motion of the Earth by providing the necessary centripetal force.

3. How does the Earth's circular motion affect its gravitational pull?

The Earth's circular motion has a direct impact on its gravitational pull. As the Earth moves in its orbit, it creates a centrifugal force that counteracts the pull of gravity. This results in a slightly weaker gravitational pull at the equator compared to the poles.

4. Is circular motion and static friction unique to the Earth?

No, circular motion and static friction are not unique to the Earth. Many other objects in the universe, such as planets, moons, and satellites, also exhibit circular motion and rely on static friction to maintain their orbits.

5. Can changes in circular motion and static friction affect the Earth's climate?

Yes, changes in circular motion and static friction can have a significant impact on the Earth's climate. For example, changes in the Earth's tilt and orbit can lead to variations in the amount of solar radiation received, which can affect the Earth's temperature and weather patterns.

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