Fictitious force – JEE First

Physics concepts and problems for the JEE

Coriolis effect and angular momentum

February 20th, 2022jeefirst0 Comments

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?

Rendered by QuickLaTeX.com

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 …

Mass on a semicircular block

February 1st, 2022jeefirst0 Comments

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.

Rendered by QuickLaTeX.com

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

Solution:

(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 …