Latitude is an angle that ranges from 0° at Earth's equator to 90° (north or south) at the poles. What is the angular speed (ω) and linear speed of a point along Earth's surface at 30° north latitude?

Answer 1

To find the angular speed (ω) and linear speed (v) of a point along Earth's surface at 30° north latitude, we will first find the Earth's angular speed and then apply formulas to find the linear speed at 30° north latitude.

The Earth rotates 360° in 24 hours (or 86400 seconds). Therefore, the Earth's angular speed (ω_earth) is:

ω_earth = 360° / 86400 s = 0.004167°/s

Now, we can convert the Earth's angular speed from degrees per second to radians per second:

ω_earth = 0.004167°/s * (π / 180) = 7.292 x 10^(-5) rad/s

The angular speed (ω) at 30° north latitude is the same as the Earth's angular speed:

ω = ω_earth = 7.292 x 10^(-5) rad/s

Now let's find the linear speed (v) at 30° north latitude. The Earth's radius (R) is approximately 6371 km, and at 30° north latitude, the effective radius (R') is equal to R * cos(30°):

R' = 6371 * cos(30°) = 6371 * (√3/2) = 5517.62 km (approximately)

Now, we can find the linear speed (v) using v = ω * R':

v = 7.292 x 10^(-5) rad/s * 5517620 m = 402.44 m/s (approximately)

So, the angular speed (ω) of a point along Earth's surface at 30° north latitude is 7.292 x 10^(-5) rad/s, and the linear speed (v) is approximately 402.44 m/s.