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# pseudo-force: Centrifugal

A caution of physics texts about usage of Newton's 2nd Law is: "Be sure to use a non-acccelerating, that is inertial coordinate reference." However, after that state­ment, through numerous examples next to nothing further is said or done regarding inertial coordinate reference selection. The examples, being in an Earth environment, does text disregard of reference imply all places on Earth are inertial?

Upon further reading one encounters a second "caution." If coordinates "not inertial (by error or choice)" are used, special "fictitious" or "pseudo" forces might be needed. Centrifugal force is the simplest case. The premise of this example is:

A "certified mass" is used to calibrated a spring scale at the North Pole.
Later, at the Equator, the spring scale shows a discrepancy using the
same mass."

North Pole Event:  The discussion below is a comparison of two "weighing events" on Earth. Each weighing by the same spring scale is assumed to be in inerial coordinates. To keep things clear a first step, Figure 1 is a setup.

In Figure 1: Earth is represented as a rotating "upright" sphere. Earth Coordinates rotate with Earth but the "North Pole" coordinate set does not to rotate. Establish Mass: System mass is established using a standard (1000kg) and a beam balance. Establish Force Scale: At the North Pole, a spring scale is calibrated while supporting the system mass.

Equator Event: Figure 2(a) depicts Earth with coordinates at the Earth center and Equator (Earth surface)coordinates. Figure 2(b) shows the (NP calibrated) spring scale supporting the system mass, 1000kg. The scale reading is 9874 Newtons.

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