Question

You sit "at rest" in front of your computer to answer this question. But you sit on the surface of a planet that spins, so even while you sit "at rest," you are really hurtling through space at high speed. The average radius of the Earth is 6378 km. Ignoring all rotations except the spin of the Earth, what is your linear speed, in kph (kilometers per hour), while you sit in your home?

Answer 1

Answer: Linear speed is 1,670 Kph.

Explanation:

If we assume that the earth is a perfect sphere, and that is spinning itself once every roughly 24 hr, we can get the angular velocity of the Earth, in magnitude, as follows:

ω = 2π / 24 Hr

Now, by definition, an angle is the relationship between the arc s, and the radius r, so we can replace these values in the angular velocity expression, as follows:

ω = (Δs / r) . 1/Δt ⇒ ω = (Δs/Δt). 1/r

But, by definition, Δs/At, is just the linear velocity, v, so we can conclude the following;

ω = v/r ⇒ v = ω. r

So, we can get v, as follows:

v = 2π /24 hr . 6378 Km = 1,670 Km/hr.