Asteroid Hits Earth Conservation of angular momentum

In summary, the Earth has an initial angular speed of 7.272 x 10^-5 rad/s and is hit by an asteroid with a mass of 1.17 x 10^22 kg traveling at 1.41 x 10^3 m/s. The final angular speed after the collision can be calculated using the equation Wf = (MaVa + 2/5MeRWe) / (Ma + 2/5MeR). However, this equation may result in a final angular speed that is faster than the Earth's initial angular speed, so further calculations or considerations may be needed. The direction of rotation may also affect the final result.
  • #1
FahimP
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0

Homework Statement



the Earth has a n angular speed of 7.272 x 10 ^ -5 rad/s in it;s rotation. Find the new angular speed if an asteroid ( m = 1.17 x 10 ^ 22kg) hits the Earth while traveling at 1.41 x10^3 m/s.
the asteroid hits the Earth dead center

Homework Equations





The Attempt at a Solution


(La)f + ( Le) f = ( La) + (Le)i
Wf( MaR + 2/5MeR^2) = maRV + 2.5MeR^2W
Wf = ( MaVa + 2/5MeRWe) / ( Ma + 2/5MeR)

this is what I have as final angular speed but it gives me an answer faster than the Earth's initial angular momentum when the books answer is slightly less than the Earth's initial answer.
 
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  • #2
What's the angular momentum of the asteroid before the collision?
 
  • #3
Hmmm, just my own question. Does the direction of the rotation matter?

Delzac
 

What is conservation of angular momentum and how does it apply to asteroid hits on Earth?

Conservation of angular momentum is a law of physics that states that the total angular momentum of a system remains constant as long as there are no external forces acting on the system. This means that if an asteroid were to hit Earth, the total angular momentum of the asteroid and Earth's rotation would remain the same before and after the impact.

Why is conservation of angular momentum important in understanding the effects of asteroid impacts?

Conservation of angular momentum is important because it helps us understand how an asteroid's impact can affect the rotation of Earth. If the asteroid has a large amount of angular momentum, it can cause Earth to spin faster or slower depending on the direction of impact. This can have significant consequences for the Earth's climate and ecosystem.

How does the size and speed of an asteroid impact affect the conservation of angular momentum?

The size and speed of an asteroid impact can greatly affect the conservation of angular momentum. A larger and faster asteroid would have a greater amount of angular momentum, meaning it could potentially cause more disruption to Earth's rotation. However, even a small and slow-moving asteroid can have a significant impact if it is able to transfer its angular momentum to Earth.

Can conservation of angular momentum be used to predict the effects of future asteroid impacts on Earth?

While conservation of angular momentum can help us understand the potential effects of asteroid impacts on Earth, it is not the only factor to consider. Other factors such as the angle and location of impact, as well as the composition of the asteroid and Earth's surface, also play a role. Therefore, it is not possible to accurately predict the exact effects of a future asteroid impact using conservation of angular momentum alone.

Are there any ways to mitigate the effects of an asteroid impact on Earth's rotation?

There are currently no known methods to directly mitigate the effects of an asteroid impact on Earth's rotation. However, scientists are constantly studying and monitoring near-Earth objects and developing strategies to potentially redirect or destroy any asteroids that may pose a threat to Earth. Additionally, early detection and warning systems can help minimize the impact on human populations in the event of an asteroid impact.

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