Math Help Forum: Linear Speed

This question has 3 parts. I've got the first two parts (I think), I just can't figure out part c. I will include the others though since it's relevant to c.

a) give the angular velocity of the Earth's rotation about it's axis in radians per hour. I got 2pi/24hr=pi/12

b) If the diameter of the Earth is 7920 miles, what is the linear speed (relative to the center of the Earth) at the equator?

v=7920/2(pi/12)=330

c) Our latitude at our campus is approximately 39.25* north. How far are we from the axis of rotation of the Earth? What is our linear speed due to the Earth's rotation?

The one I have no idea. There is a graph with the triangle in it, but I still don't know what to do with it.

Thank you!

Originally Posted by Chinnie15

This question has 3 parts. I've got the first two parts (I think), I just can't figure out part c. I will include the others though since it's relevant to c.

a) give the angular velocity of the Earth's rotation about it's axis in radians per hour. I got 2pi/24hr=pi/12

is correct.

b) If the diameter of the Earth is 7920 miles, what is the linear speed (relative to the center of the Earth) at the equator?

v=7920/2(pi/12)=330

Should be

c) Our latitude at our campus is approximately 39.25* north. How far are we from the axis of rotation of the Earth? What is our linear speed due to the Earth's rotation?

Use a coordinate system with the Earth's center as the origin, the equator as the x-axis and the axis of rotation as the y-axis. Your campus would be directly over the x-axis on the surface of the Earth. Your latitude is then the angle between the x-axis and a ray passing through your campus. Is this what your given triangle looks like? Check out the drawing I've attached.

Your distance from the Earth's axis of rotation is the x-coordinate of this point on the coordinate system (assuming a spherical Earth). How can you find this x-coordinate?

Your angular speed is the same as it would be on the equator, right? Once you know how far you are away from the axis of rotation, how can you find your linear speed?

Yes, that is what my graph looks like.

Oh ok, so, would I take the sin of 39.25?

Thank you very much for your help!

The sine (times the radius) gives you the y-coordinate. You want the cosine (times the radius).
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