What is the linear speed of a point:

a) on the equator,
b) on the Arctic Circle (latitude 66.5 degrees N),
c) at a latitude of 45.0 degrees N, due to the Earth's rotation?

a relevant equation is v=rw, but I'm not sure how to apply it to the equation

464m/s

I like it

w = 2 pi/24 radians.hr = 2 pi/(24*3600) radians/second

R = earth radius in meters (3.4*10^6 m)

r = distance from spin axis of earth = R * cos (latitude)

6.4 * 10^6 not 3.4 *10^6

(remembered Mars, not earth)

To find the linear speed of a point on the Earth's surface due to its rotation, you can use the equation v = rω, where v is the linear speed, r is the distance from the point to the Earth's axis of rotation, and ω (omega) is the angular speed of the Earth's rotation.

a) On the equator:
At the equator, the distance from the point to the Earth's axis of rotation (r) is equal to the radius of the Earth (R). The angular speed of the Earth's rotation (ω) is approximately 7.2921159 × 10^-5 radians per second. So, you can calculate the linear speed (v) at the equator using the equation v = Rω.

b) On the Arctic Circle:
At the Arctic Circle, the distance from the point to the Earth's axis of rotation (r) is equal to the radius of the Earth (R). The angular speed of the Earth's rotation (ω) remains the same as on the equator. So, you can use the equation v = Rω to calculate the linear speed at the Arctic Circle as well.

c) At a latitude of 45.0 degrees N:
To find the distance from the point to the Earth's axis of rotation (r) at a latitude of 45.0 degrees, you can use the equation r = R * cos(latitude), where R is the radius of the Earth and latitude is the given latitude in degrees.
After finding the value of r, you can use the equation v = rω to calculate the linear speed at this latitude.

Remember to convert the latitude from degrees to radians when using it in the equations.

YEEEEEEEEEET