Coriolis effect and angular momentum

Imagine a mass m moving on the surface of a rotating sphere. For instance, the mass could be parcel of air moving away from a high pressure region in the Earth’s atmosphere. It experiences a Coriolis force which, in the example shown in the figure below, pushes it from its original trajectory (orange) to move eastward (blue). Why does this happen, and how do we understand it intuitively?

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Formally, the Coriolis force on m is given by

(1)   \begin{equation*}   {\bf F}_{\rm Coriolis} = - 2 m {\bf \Omega} \times {\bf v}_{\rm rot} ,  \end{equation*}

where {\bf \Omega} is the angular velocity of the rotating frame (Earth), and {\bf v}_{\rm rot} is the velocity of m as seen by an observer on the Earth’s …

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Mass on a semicircular block

A heavy particle of mass m is placed at the top of a semicircular block of radius R. Find the height at which the particle falls off, assuming (i) the block is fixed to the ground, and (ii) the block has a mass M and is free to move. Assume all surfaces are frictionless.

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Related problem: Sliding on a block with a circular cut.


(i) We first consider the case where the block is fixed to the ground. As the mass slides down the block, there are three forces acting on it: the weight mg, the centrifugal force m R \dot{\theta}^2, and …

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