Calculate the acceleration due to the rotation of the Earth of a person in a location 22° northern geographical latitude. Use R
Earth
= 3,680 km for the value of the radius of the Earth.
0.0195
To calculate the acceleration due to the rotation of the Earth for a person at a specific location, we can use the formula:
a = Rω^2cosθ
Where:
a is the acceleration due to rotation
R is the radius of the Earth
ω (omega) is the angular velocity of the Earth's rotation
θ (theta) is the latitude of the location
Given that R Earth = 3,680 km and θ = 22°, we'll first need to convert the values to the appropriate units:
R = 3,680 km = 3,680,000 meters
θ = 22° = 22 × π/180 radians (since the formula requires radians)
Now, let's find the angular velocity (ω) using the formula:
ω = 2π/T
Where T is the time taken for one complete rotation of the Earth. The average period of rotation of the Earth is approximately 24 hours.
Substituting the values, we have:
ω = 2π/24 hours = 2π/(24 × 60 × 60 seconds) = π/43,200 rad/s
Now, we can calculate the acceleration:
a = (3,680,000 meters) × (π/43,200 rad/s)^2 × cos(22 × π/180)
Calculating this expression will give us the acceleration due to the rotation of the Earth at a location 22° northern geographical latitude.