# Effect of earth's rotation on an object on the surface

• timarli
In summary, the conversation discusses the total force on an object on the surface of the Earth, taking into account both gravity and the Earth's rotation. The conversation also mentions the concept of normal force and how it relates to the net force. Ultimately, the conversation emphasizes the importance of using kinematics to determine the net force on an object, rather than focusing on the individual forces.
timarli
Hi,

This is one of the things that confuses me.

Assume an object on the surface of the Earth has a mass m and F=m*g is the force on it due to the gravity. But also the Earth is rotating and although the radius is extremely large compared to the size of the object but it must be affected by this rotation as well, isn't it?

This is the part that I couldn't figure out. What is the total force on the body?

Is it:

(G*m*M/R^2) - (m*v^2/R); obviously first one gravity component and the second one angular acceleration.

timarli said:
What is the total force on the body?

Is it:

(G*m*M/R^2) - (m*v^2/R); obviously first one gravity component and the second one angular acceleration.
No.

Look at the problem kinematically:
• What kind of motion does an object on the surface of the Earth undergo from the perspective of an inertial observer?
Ignore the Earth's orbit about the Sun. (e.g., use a frame in which the Earth is rotating but the center of mass is stationary.)
• What is the acceleration of the object from the perspective of this inertial observer?
• What does Newton's second law say that the total force must be?

Thanks a lot for the response D H. I will try to answer in the same order;

D H said:
• What kind of motion does an object on the surface of the Earth undergo from the perspective of an inertial observer?
Ignore the Earth's orbit about the Sun. (e.g., use a frame in which the Earth is rotating but the center of mass is stationary.)
OK, it's only Earth and the object and the observer. The observer looking from the top.
The object is undergoing a uniform angular motion.

D H said:
• What is the acceleration of the object from the perspective of this inertial observer?
The acceleration is a=v^2/R

D H said:
• What does Newton's second law say that the total force must be?
F = m*a

And the only acceleration is the angular one (v2/R); so the Earth pulls the object due to gravity and the object pulls Earth equally (as if the Earth is stationary - Newton #3). But then there is the rotational acceleration which means there is some unbalanced force. Earth is pulling the object more than the object pulls her.

Am I correct in thinking that;

N - m*M*G/R^2 = m*v^2/R

Even if it's correct, still not clear on the N though.

timarli said:
Hi,

This is one of the things that confuses me.

Assume an object on the surface of the Earth has a mass m and F=m*g is the force on it due to the gravity. But also the Earth is rotating and although the radius is extremely large compared to the size of the object but it must be affected by this rotation as well, isn't it?

This is the part that I couldn't figure out. What is the total force on the body?

Is it:

(G*m*M/R^2) - (m*v^2/R); obviously first one gravity component and the second one angular acceleration.

That would be the weight of the mass as measured by a scale, on the equator. But not the total force.

Remeber that a mass resting on the Equator has net force applied to it close, but not equal to, zero (gravity pulling it in, the Earth pushing it out almost with the G force, the difference being your mv^2/R.

timarli said:
OK, it's only Earth and the object and the observer. The observer looking from the top.
The object is undergoing a uniform angular motion.
Correct.

The acceleration is a=v^2/R
Correct.

F = m*a
Correct. You know m, you know a, so what does that mean that the net force F must be? This is kinematics, not dynamics. You don't need to know *anything* about causal agents such as gravity. Just use F=ma.

But then there is the rotational acceleration which means there is some unbalanced force.
Exactly. Gravitation obviously is not the only force acting on an object sitting at rest (with respect to the rotating Earth) on the surface of the Earth. There's also a force that keeps the object object from sinking into the Earth. This is the same force that keeps your hand from penetrating into a wall when you lean against a wall, and that keeps your hand from penetrating into a book when you hold the book from beneath. It's called the normal force.

If you know the acceleration of some object, you do not need to know the individual contributors to the net force. Simply apply Newton's second law and the net force just pops out. In fact, you need to compute this net force kinematically to determine the normal force. You know the net force, you know the gravitational force, and assuming that the only other force, you can compute the normal force based on the fact that forces are subject to the superposition principle (net force is the vector sum of the individual component forces).

## 1. How does the rotation of the Earth affect the motion of an object on its surface?

The rotation of the Earth causes a force known as the Coriolis force, which can impact the motion of objects on the surface. This force is caused by the Earth's rotation and the curvature of its surface, and it can cause objects to deviate from a straight path, especially at high speeds.

## 2. Does the direction of rotation of the Earth affect the behavior of objects on its surface?

Yes, the direction of rotation of the Earth can have an impact on the behavior of objects on its surface. In the Northern Hemisphere, the Coriolis force tends to deflect objects to the right, while in the Southern Hemisphere, it deflects objects to the left. This is due to the direction of the Earth's rotation and the orientation of its axis.

## 3. How does the Earth's rotation affect the trajectory of moving objects?

The Earth's rotation can cause moving objects to have a curved trajectory, rather than a straight line. This is due to the Coriolis force, which can change the direction of an object's motion as it moves across the Earth's surface. This effect is most noticeable over long distances and with high-speed objects.

## 4. Can the Earth's rotation affect the speed of objects on its surface?

Yes, the rotation of the Earth can affect the speed of objects on its surface. The Coriolis force can either add to or subtract from the speed of an object, depending on its direction of motion and the direction of the Earth's rotation. This effect is most significant for objects moving over long distances and at high speeds.

## 5. Is the effect of the Earth's rotation on objects on its surface significant in everyday life?

In most cases, the effect of the Earth's rotation on objects on its surface is not noticeable in everyday life. However, it can have a significant impact on large-scale phenomena such as weather patterns and ocean currents. It is also important to consider when launching rockets or satellites, as the Coriolis force can affect their trajectory.

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