B M Sharma Solutions for Chapter: Rigid Body Dynamics: Part 2, Exercise 1: CONCEPT APPLICATION EXERCISE

A particle of mass $m$ is released from rest at point $A$ in figure, falling parallel to the (vertical) $y$-axis. Find the angular momentum of the particle at any time $t$ with respect to the same origin $O.$ Let acceleration due to gravity is $g$.

A paricle of mass $m$ is projected with a speed $u$ at an angle $\mathrm{\theta }$ to the horizontal at time $t=0$. Find is angular momentum about the point of projection $o$ at time $t$, vectorially. Assume the horizontal and vertical lines throught $O$ as $X$ and $Y$ axes, respectively.

A circular disc of mass $m$ and radius $R$ is set into motion on a horizontal floor with a linear speed $v$ in the forward direction and an angular speed $w=v/R$ in the clockwise direction as shown in figure. Find the magnitude of the total angular momentum of the disc about the bottommost point $O$ of the disc.

Calculation the angular momentum about $"O"$ on the axis of rotation in following cases.
(i)  (ii) 

Calculation the angular momentum in following situation a disc is connected with a rod mass $m$ and length; $l.$ The disc is free to rotate about its own axis. If whole system is rotating with ${\omega }_1\widehat{j}$ and disk also rotate about its own axis with ${\omega }_2\widehat{i}$ then calculation $\overrightarrow{L}$ about origin.

A sphere rolls without slipping on a rough surface with centre of mass has constant speed $v_0$ if mass of the sphere is $M$ and its radius be $R,$ then find the angular momentum of the sphere about the point of contact.