Consider a point A on the surface of the earth at north latitude L. The radius of the eart...

Consider a point A on the surface of the earth at north latitude L. The radius of the earth is RE, and the earth’s angular velocity is ωE. A plumb bob suspended just above the ground at point A will hang at a small angle β relative to the vertical because of the earth’s rotation. Show that β is related to the latitude by

Strategy: Using the earth-fixed coordinate system shown, express Newton’s second law in the form given by Eq. (17.22).