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https://texercises.com/exercise/asteroid/
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Exercise:
An asteroid of mass pq.ekg travelling at a speed of pqk relative to the Earth hits the Earth at the equator tangentially and in the direction of Earths rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.

Solution:
Angular momentum will be conserved in the Earth-Asteroid system. Asing the asteroid becomes embedded in the Earth at the surface the Earth and the asteroid will have the same angular velocity after the collision. If we ase the Earth to be an ideal sphere and the asteroid to be a po mass we get: L_ L_ I_EarthIndex omega_EarthIndex + I_a omega_a I_EarthIndex + I_a omega The percent change in the angular speed of the Earth omega_EarthIndex is therefore: fracomega-omega_EarthIndexomega_EarthIndex fracI_a omega_aI_EarthIndex omega_EarthIndex fracm_a r_EarthIndex^ fracv_ar_EarthIndexfrac m_EarthIndexr_EarthIndex^ omega_EarthIndex numpr. That is numpr.% hence no change to notice.
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\(\LaTeX\)-Code
Exercise:
An asteroid of mass pq.ekg travelling at a speed of pqk relative to the Earth hits the Earth at the equator tangentially and in the direction of Earths rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.

Solution:
Angular momentum will be conserved in the Earth-Asteroid system. Asing the asteroid becomes embedded in the Earth at the surface the Earth and the asteroid will have the same angular velocity after the collision. If we ase the Earth to be an ideal sphere and the asteroid to be a po mass we get: L_ L_ I_EarthIndex omega_EarthIndex + I_a omega_a I_EarthIndex + I_a omega The percent change in the angular speed of the Earth omega_EarthIndex is therefore: fracomega-omega_EarthIndexomega_EarthIndex fracI_a omega_aI_EarthIndex omega_EarthIndex fracm_a r_EarthIndex^ fracv_ar_EarthIndexfrac m_EarthIndexr_EarthIndex^ omega_EarthIndex numpr. That is numpr.% hence no change to notice.
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Attributes & Decorations
Branches
Momentum
Tags
angular, asteroid, conservation, inertia, law, mechanics, moment, momentum, of, physics, rotation
Content image
Difficulty
(3, default)
Points
4 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link