Linear speed

Question

Earth rotates on an axis through its poles. The distance from the axis to a location on Earth at 40 degrees north latitude is about 3033.5 miles. Therefore a location on Earth at 40 degree north latitude is spinning on a circle of radius 3033.5 miles. Compute the linear speed on the surface of the Earth at 40 degrees north latitude.

Answer 1

Hi Sally!

 

The key to this is the relationship, in uniform circular motion (circular motion at a constant speed), between the linear speed (v) of an object on a circular path, and its angular speed (ω).  If the angular speed is in radians per second, that relationship is:

 

v = rω

 

where

 

r = radius of circle

 

This helps because, for any point on the surface of the Earth, we basically know the angular speed in radians per second, because we know the number of radians in a complete revolution, and the time it takes to go around a complete revolution.  Then:

 

ω = [radians in a revolution]/[time to make one revolution]

 

Since the radius of the circular path is given, you can then compute v = rω.

 

I hope this helps get you on your way!  Please let me know if you would like to look at this more closely.