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 w and linear speed of a point along Earth's surface at 30° north latitude?

1 answer

To find the angular speed (w) at 30° north latitude, we first need to know the Earth's angular speed. The Earth takes approximately 24 hours to complete a full rotation of 360° around its axis. Therefore:

w_earth = 360° / (24 hours) = 15° per hour

Since the angular speed is the same everywhere on Earth, the angular speed (w) at 30° north latitude is also:

w = 15° per hour

Next, we need to find the linear speed (v) at 30° north latitude. To do this, we first calculate the radius (r) of the circle at 30° north latitude using Earth's radius (R):

R = 6371 km (approximate Earth's radius)
r = R × cos(latitude)
r = 6371 km × cos(30°)
r ≈ 5520.571 km

Now we can calculate the circumference (C) of the circle at 30° north latitude:

C = 2 × π × r
C ≈ 2 × π × 5520.571 km
C ≈ 34,669.991 km

Since the Earth takes 24 hours to complete a full rotation (360°), the linear speed at 30° north latitude is:

v = C / (24 hours)
v ≈ 34,669.991 km / 24 hours
v ≈ 1444.583 km/h

Thus, the angular speed (w) at 30° north latitude is 15° per hour, and the linear speed (v) is approximately 1444.583 km/h.