Momentum of an asteroid / Earth

In summary, the conversation discusses using angular momentum to find the percentage change in the angular speed of the Earth when an asteroid strikes it tangentially in the direction of the Earth's rotation. The approach involves understanding the definitions of angular momentum and linear momentum for both the asteroid and the Earth. The relationship between the angular momentum of the Earth and the linear momentum of the asteroid is not clear and requires further explanation.
  • #1
canvas01
1
0
Please help me to understand this question: I'm paraphrasing it. A speed (relative to earth) and mass for an asteroid are given, and the asteroid strikes the Earth tangentially in the direction of the Earth's rotation at the equator. The question tells us to use angular momentum to find the percentage change in the angular speed of the earth.

My approach: Because the asteroid is not rotating, it has no angular momentum, just linear momentum represented as mv. The Earth however, has no linear momentum, just angular momentum which is equal to Iw where I = .4mr^2 and w = v/r where v = circumference of the earth/time of one complete rotation of the earth. I'm confused as to where to go from here? How are the angular momentum of the Earth and the linear momentum of the asteroid related?
 
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  • #2
canvas01 said:
Please help me to understand this question: I'm paraphrasing it. A speed (relative to earth) and mass for an asteroid are given, and the asteroid strikes the Earth tangentially in the direction of the Earth's rotation at the equator. The question tells us to use angular momentum to find the percentage change in the angular speed of the earth.

My approach: Because the asteroid is not rotating, it has no angular momentum, just linear momentum represented as mv. The Earth however, has no linear momentum, just angular momentum which is equal to Iw where I = .4mr^2 and w = v/r where v = circumference of the earth/time of one complete rotation of the earth. I'm confused as to where to go from here? How are the angular momentum of the Earth and the linear momentum of the asteroid related?
The asteroid does have angular momentum relative to the rotation axis of the earth. What is the definition of angular momentum? (It is not Iω; that is derived from the definition applied to a rotating rigid object)
 
  • #3


To answer this question, we need to understand the concept of conservation of momentum. This principle states that the total momentum of a system remains constant unless acted upon by an external force.

In this scenario, the system consists of the asteroid and the Earth. Before the impact, the asteroid has a certain linear momentum due to its mass and speed, while the Earth has a certain angular momentum due to its mass and rotational speed. As the asteroid strikes the Earth tangentially, it transfers its linear momentum to the Earth, causing it to gain linear momentum in the same direction.

However, this also affects the Earth's angular momentum. As the asteroid's linear momentum is transferred to the Earth, it also causes a change in the Earth's rotational speed. This is because angular momentum is a product of both mass and rotational speed, and any change in either of these factors will result in a change in angular momentum.

To calculate the percentage change in the Earth's angular speed, we can use the equation:

% change in angular speed = (change in angular speed/original angular speed) x 100

In this case, the change in angular speed is caused by the transfer of linear momentum from the asteroid, and we can calculate it using the equation:

Change in angular speed = (linear momentum of asteroid/total moment of inertia of Earth) x original angular speed

Substituting the values given in the question, we can calculate the percentage change in the Earth's angular speed. This will give us a measure of how much the Earth's rotational speed has increased due to the impact of the asteroid.

In summary, the angular momentum of the Earth and the linear momentum of the asteroid are related through the principle of conservation of momentum. The transfer of linear momentum from the asteroid to the Earth causes a change in the Earth's angular momentum, which can be calculated using the equations mentioned above.
 

1. What is momentum?

Momentum is a measure of an object's motion. It is calculated by multiplying an object's mass by its velocity.

2. How is momentum related to an asteroid or the Earth?

Momentum is related to an asteroid or the Earth because it is a property that all objects with mass and velocity possess. The momentum of an object can change if its mass or velocity changes.

3. How is momentum conserved in the motion of an asteroid or the Earth?

Momentum is conserved in the motion of an asteroid or the Earth because of the law of conservation of momentum. This law states that the total momentum of a closed system remains constant, meaning that the total momentum of the asteroid and the Earth will remain the same unless an external force acts on them.

4. How does the momentum of an asteroid affect its path in space?

The momentum of an asteroid affects its path in space because it determines the direction and speed at which the asteroid will travel. If an external force, such as gravity from another object, acts on the asteroid, its momentum will change and therefore affect its path.

5. Can the momentum of an asteroid or the Earth be changed?

Yes, the momentum of an asteroid or the Earth can be changed. This can occur if an external force, such as a collision or gravitational pull, acts on the object. The object's mass or velocity can also be changed, which will also affect its momentum.

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