Just as our earth completes one rotation in 24Hrs on its polar axis, our moon ro

Question

Just as our earth completes one rotation in 24Hrs on its polar axis, our moon rotates once in 27.3 earth days (2,358,720 seconds) through its polar axis. An asteroid of mass mast is swiftly moving on the moon’s equatorial plane. The asteroid makes a perfect inelastic collision with the moon on the moon’s equator at the location shown in the figure below. What is the required collision linear momentum of the asteroid just before impact, in order that the asteroid completely stops the moon from rotating on its polar axis? Consider the moon as a uniform solid spherical object whose “center – of – mass†is at the center of the moon. Mmoon = 7.36 x 1022 kg and Rm = 1.74 x 106 meters.

Explanation / Answer

speed of asteroid be such that angular momentum becomes 0 after collision
thus angular momentum anre equal and opposite
this implies
I*omega=m*v*r
thus m*v= I*omega/r I=2Mr^2/5
M*v= 1.36*10^23 kgm/s

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