Earth's rotation and gravitation

In summary, the book defines centripetal force and gravitational force as two separate forces acting in opposite directions. The net centripetal force on an object at the Earth's equator is less than the normal force due to the Earth's rotation. This is because the centrifugal acceleration acts in the opposite direction of the gravity, causing a decrease in the normal force.
  • #1
quasi426
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I don't understand why the physics book defines the centripetal force and gravitational force acting in different directions.

N - m*(acceleration of gravity) = -m*r*w^2

N = m*(acceleration of gravity) - m*r*w^2

Why don't the acceleration of gravity and centripetal acceleration add up? I would think that the normal force would be greater near the equator since there is both gravitational and centripetal forces in the same direction. But the book says the opposite. Thanks for the help.
 
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  • #2
Centripetal force is not a kind of force, it is just the name given to any force that pulls towards the center of some rotating system. (Centripetal just indicates the direction of the force, not the source of the force. It's similar to saying that a force acts horizontally or vertically. Centripetal means "towards the center".)

In the case of an object at the equator, the net centripetal force is just the net force acting towards the center. If the Earth didn't rotate, then there would be zero acceleration and N = mg. But the Earth does rotate, so there must be a net force acting centripetally on the object. Thus the normal force is less. If the Earth starting spinning faster and faster, at some point the object would be thrown off--the normal force would go to zero.

Looked at from the noninertial frame of the rotating Earth you can say that there is a centrifugal acceleration on the object that acts to pull the object away from the center. (Centrifugal means "away from the center".) So you could say that the acceleration due to gravity and the centrifugal acceleration add up, but they act in opposite directions.
 
  • #3


I can understand your confusion about the relationship between Earth's rotation and gravitation. Let me explain it in a simple way.

Firstly, the centripetal force and gravitational force are two different concepts. The centripetal force is the force that keeps an object moving in a circular path, while the gravitational force is the force of attraction between two objects with mass. In the case of Earth's rotation, the centripetal force is provided by the gravitational force between Earth and the object on its surface.

In the equation you provided, N represents the normal force, which is the force exerted by a surface on an object in contact with it. The first part of the equation, m*(acceleration of gravity), represents the force of gravity pulling the object towards the center of Earth. The second part, -m*r*w^2, represents the centripetal force acting in the opposite direction to keep the object in its circular path.

Now, to address your question about the acceleration of gravity and centripetal acceleration not adding up, it is important to note that they are two different types of acceleration. The acceleration of gravity is the acceleration due to the gravitational force, while the centripetal acceleration is the acceleration due to the centripetal force. They are not added together because they are acting in different directions.

As for your observation about the normal force being greater near the equator, it is correct. This is because the centripetal force is greater at the equator due to the Earth's rotation, and thus the normal force must be greater to balance it out and keep the object in equilibrium.

I hope this explanation helps to clarify the relationship between Earth's rotation and gravitation. It is a complex concept, but understanding it is crucial in understanding the motion of objects on Earth's surface. If you have any further questions, please do not hesitate to ask.
 

1. How does the rotation of the Earth affect the length of a day?

The rotation of the Earth on its axis is what causes day and night. As the Earth rotates, different parts of it are exposed to the sun's light, creating the cycle of day and night. The rotation of the Earth also affects the length of a day, as it takes 24 hours for the Earth to make one full rotation, resulting in a 24-hour day.

2. What is the difference between rotation and revolution?

Rotation refers to the Earth spinning on its axis, while revolution refers to the Earth's orbit around the sun. The Earth rotates once every 24 hours, causing day and night, while it takes approximately 365.24 days to complete one revolution around the sun, resulting in a year.

3. How does gravity keep objects on Earth?

Gravity is the force that keeps objects on Earth from floating away into space. Gravity is created by the Earth's mass, and it pulls objects towards its center. The strength of gravity depends on the mass of the object and its distance from the center of the Earth.

4. How does the Earth's rotation and gravity affect the tides?

The Earth's rotation and gravity play a significant role in the formation of tides. As the Earth rotates, it creates a bulge of water on the side facing the moon and a bulge on the opposite side. This creates high tides in those areas. At the same time, areas in between experience low tides due to the water being pulled away from them.

5. Can the Earth's rotation and gravity change over time?

Yes, the Earth's rotation and gravity can change over time. The rotation of the Earth can slow down or speed up due to factors like the moon's gravitational pull or changes in the Earth's shape. Similarly, the strength of gravity can vary due to changes in the Earth's mass or its distance from other objects in space.

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