@@ -324,12 +324,12 @@ Paris is not on the North pole, but it does lie on the Northern hemisphere, so t
1. Suppose that you enter the Panthéon at noon, and mark the direction in which the pendulum is oscillating. When you return an hour later, by how much will this plane have rotated? Will this be enough to be visible by eye? The Panthéon is at $48^\circ50'46''\mathrm{N}$ (note that degrees, like hours, are divided in (arc)minutes and seconds that run up to 60, not 100).
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```{exercise}
```{exercise} Fictitious forces on a sliding particle
:class: dropdown
An alternative way to show the effect of the rotation of the Earth involves only a smooth horizontal plane and a particle that can slide over it. Show that if the particle's velocity is $v$, its trajectory will be a circle with radius $r = v/2\Omega$, where $\Omega$ is the Earth's rotational velocity.
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````{exercise}
````{exercise} Parabolic water surface
:label: pb:parabolicwatersurface
:class: dropdown
The centrifugal force emerges in a rotating coordinate frame, and famously causes the parabolic shape of the surface of water in a rotating bucket. As the centrifugal force is always perpendicular to the rotation axis, we can pick coordinates such that the rotation axis coincides with the $z$-axis, $\bm{\omega} = \omega \bm{\hat{z}}$, and we can express the centrifugal force in cylindrical coordinates as $\bm{F}_\mathrm{cf} = m \omega^2 \rho \bm{\hat{\rho}}$ (equation {eq}`centrifugalcylindrical`).
