If Earth somehow contracted to of its current volume instantly (through some magical internal forces), while keeping its shape and mass, then how long would a day be?(No useless answers please!)
Answers
Since only internal forces are shrinking it, the angular momentum of Earth will remain constant.
Volume is proportional to r³
Therefore, 1/8th volume = (1/8)r⅓ = r/2
Angular momentum (L) = IW , where I is the moment of inertia and W is the angular velocity
I proportional to mr²
If radius is halved, I will become ¼th, thus W should become 4 times.
Hence, the earth will spin 4 times as fast, making the time of a day = 24/4 = 6 hours
☺️
Answer:
Since only internal forces are shrinking it, the angular momentum of Earth will remain constant.
Volume is proportional to r³
Therefore, 1/8th volume = (1/8)r⅓ = r/2
Angular momentum (L) = IW , where I is the moment of inertia and W is the angular velocity
I proportional to mr²
If radius is halved, I will become ¼th, thus W should become 4 times.
Hence, the earth will spin 4 times as fast, making the time of a day = 24/4 = 6 hours
☺️