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?
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.
To determine the angular speed and linear speed of a point on Earth's surface at a specific latitude, we can use the following formulas:
1. Angular speed (ω) is the rate at which an object rotates around a central axis. In this case, we'll consider the rotation of Earth.
The formula for angular speed is given by:
ω = 2π/T
Where ω is the angular speed in radians per second, and T is the time taken for one complete rotation.
2. Linear speed refers to the speed of an object moving along a circular path. In the case of Earth, it refers to the speed of a point along the surface.
The formula for linear speed is given by:
v = rω
Where v is the linear speed, r is the radius of Earth, and ω is the angular speed.
Now, let's calculate the angular speed and linear speed at 30° north latitude.
Step 1: Calculate the time taken for one complete rotation (T).
Earth completes one rotation in approximately 24 hours or 86400 seconds.
T = 86400 seconds
Step 2: Calculate the angular speed (ω).
ω = 2π/T
ω = 2π/86400
ω ≈ 7.27 x 10^(-5) radians per second
Step 3: Calculate the radius of Earth (r).
The average radius of Earth is approximately 6,371 kilometers or 6,371,000 meters.
r = 6,371,000 meters
Step 4: Calculate the linear speed (v).
v = rω
v = 6,371,000 x 7.27 x 10^(-5)
v ≈ 463.03 meters per second
Therefore, at 30° north latitude, the angular speed (ω) is approximately 7.27 x 10^(-5) radians per second, and the linear speed (v) is approximately 463.03 meters per second.
To calculate the angular speed (ω) and linear speed of a point along Earth's surface at a specific latitude, we'll need the rotational speed of the Earth and the radius at the given latitude.
1. The rotational speed of the Earth (ω) is approximately 0.0000727 radians per second. This value is constant regardless of latitude.
2. The radius of the Earth changes depending on the latitude. To calculate the radius at a specific latitude:
a. Use the formula: r = R * cos(latitude), where R is the average radius of the Earth (approximately 6,371 kilometers).
b. Substituting the given latitude of 30° north, we get: r = 6,371 km * cos(30°) ≈ 5,511.7 kilometers.
3. Now that we have the values of ω (0.0000727 radians per second) and r (5,511.7 kilometers), we can calculate the linear speed using the formula:
v = ω * r
v = 0.0000727 radians per second * 5,511.7 kilometers
Convert radians per second to kilometers per second:
1 radian ≈ 111.32 kilometers
So, v ≈ 0.0000727 * 5,511.7 * 111.32 kilometers per second.
Therefore, the linear speed of a point along Earth's surface at 30° north latitude is approximately 43.148 kilometers per second.