In the apparent-weight model, what does a bathroom scale read: \(mg\), \(m\vec g\), or the normal reaction \(N\)?

Is the rotational correction to apparent weight largest at the equator or at the poles?

At latitude \(\lambda=60^\circ\), write the distance \(r_\perp\) from Earth's rotation axis in terms of Earth's radius \(R\).

Using \(\omega=7.29\times10^{-5}\,\mathrm{rad\,s^{-1}}\) and \(R=6.37\times10^6\,\mathrm{m}\), find the equatorial reduction in scale reading for a \(75\,\mathrm{kg}\) person compared with \(mg\).

At latitude \(45^\circ\), what fraction of the equatorial rotational correction remains?

A \(70\,\mathrm{kg}\) person stands where \(g=9.81\,\mathrm{N\,kg^{-1}}\). Find \(N\) at the equator using \(\omega^2R=0.0339\,\mathrm{m\,s^{-2}}\).

At what latitude is the rotational correction to apparent weight half its equatorial value?

A \(60\,\mathrm{kg}\) object has a scale reading \(2.0\,\mathrm{N}\) larger at the pole than at the equator. Estimate Earth's angular speed using \(R=6.37\times10^6\,\mathrm{m}\).

Show that the scale reading at latitude \(\lambda\) differs from the equatorial scale reading by \(m\omega^2R\sin^2\lambda\).

In the spherical-Earth model, derive the angular speed \(\omega\) that would make the scale reading zero at latitude \(\lambda\). State where the expression fails physically or mathematically.