two observers, one planet

The Force You Summon by Turning

Half the internet says centrifugal force is fake: "it is just inertia; the real force is centripetal." Both camps are right in the frame where they are speaking. Hold the motion still, change the observer, and the disputed force appears exactly where the equations require it.

Instrument A: the same puck, two frames

omega squared r = 39.478 m/s2 = 4.026 standard g

In the lab frame the puck accelerates toward the centre. The string tension is the force doing that job. "Centripetal" names the inward role; it is not another force to draw beside tension. Ride beside the puck and it is stationary relative to you. Your rotating coordinates need an outward centrifugal term of equal magnitude so that the stationary puck has zero acceleration in those coordinates.

That term is frame-dependent. It is not the Newton's-third-law pull of the puck on the string, which acts on a different body. In a turning car, what your body directly feels is the door or seat pushing inward.

The alleged fake is inside official gravity

GRS80, the reference system adopted for geodetic work, defines a rotating, equipotential ellipsoid. Its normal gravity is the gradient of the total normal potential, including the centrifugal potential. The gravitational potential alone is what remains after that centrifugal potential is subtracted. Drag latitude and Somigliana's closed formula does the calculation from the published constants.

Instrument B: normal gravity on GRS80
9.7803267715 m/s2
Somigliana normal gravity at the ellipsoid

70 kg pole-referenced scale: 69.63079 kg, down 369.21 g

direct omega squared a cos squared phi = 0.033915706 m/s2
gamma(phi) = gamma_e (1 + k sin squared phi) / sqrt(1 - e squared sin squared phi)

At the equator, normal gravity is 0.52745% below its polar value. A 70 kg mass on an ideal scale referenced to the polar reading changes by 369.21 g in kilogram-equivalent display, not in mass. The direct centrifugal term is 0.033915706 m/s2, or 65.40% of the total gap. The remaining gap reflects the oblate reference ellipsoid and its mass distribution. The split is a useful overlay, not a clean causal partition: rotation and figure are coupled in the equilibrium model.

The ellipsoid's axes differ by 21.3847 km. That bulge is consistent with a rotating equilibrium Earth, but GRS80 specifies a reference figure; this page does not pretend to derive Earth's geology or formation history from the axis difference alone.

Turn the day until the scale reaches zero

Extrapolation, not an Earth fact. This control freezes the GRS80 shape and inferred equatorial gravitation, then changes only rotation. A real faster Earth would reshape and redistribute mass.

frozen-shape equatorial effective gravity = 9.7803 m/s2

g effective = (gamma_e + omega_GRS80 squared a) - omega_day squared a. Zero at 1.4070 h.

The check

The browser and offline verifier independently recompute the displayed results from the relations and constants above.

Inputs treated as definitions or data: the GRS80 constants and ellipsoid, plus conventional standard g. Free choices: a 1 m string, the selected rpm, and a 70 kg example mass. Model boundary: Somigliana describes normal gravity on the reference ellipsoid, not local gravity anomalies, altitude, tides, weather, or a particular scale's calibration. The direct centrifugal overlay uses omega squared a cos squared phi and is not an exact decomposition of the total latitude gap. The short-day control freezes a shape that would not remain frozen.

In general relativity, gravity also joins the inertial-force family locally. The useful question was always which frame and which equations, not a vote on realness.