A spherical planet (centered at the origin of our coordinate system) of radius 5

Question

A spherical planet (centered at the origin of our coordinate system) of radius 5420km and mass 8.3x1023 kg spins with an angular velocity of w=2.5x10-6 rad/s. An asteroid of mass 9.5x1018 kg and velocity -270,000 m/s collides tangentially with the planet at its equator, (at the point (0,5.42x106,0) and becomes lodged in the planet's crust. Calculate the angular momentum of the planet (with the asteroid) and the angular velocity, about the center of the planet immediately after the collision. (assume the planet has a uniform density before the collison).

Explanation / Answer

given spherical planet

r = 5420,000 m

m = 8.3*10^23 kg

w = 2.5*10^-6 ra/s

M = 9.5*10^18 kg

v = -270,000 m/s collides tangentially at equator

a. from conservation of angular momentum

intiial angular momentum = 2*mr^2*w/5 + Mr*v

L = 9.75295*10^36 kg m^2/s

this will be final angular momentum afte rcollision as well form conservation of angular momentum

now, final angular speed = w'

hence

(2mr^2/5 + Mr^2)w'= 9.75295*10^36

w' = 0.99996 ra/s

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