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How Fast are You Spinning?

The angular speed of someone spinning should be (basically) constant regardless of where the person is (their latitude or longitude). However, their linear speed will change. Why? According to NASA's website Earth has a mean radius of 3,958.8 miles. How can you find the linear speed of someone on the equator? How can you find the linear speed of someone not on the equator? Examine the applet below and use what you know about right triangles to find the smaller radius (green line) given the latitude.