Question

A rod of mass \(m\) and lenght \(l\) is rotating about a fixed point on the ceiling. It angular velcoity is \(\omega\) with respect to vertical axis as shown in the figure. The rod maintains a constant angle \(\theta\) with the vertical.


What will be the horizontal component of angular momemtum of the rod about the point of suspension in terms of \(m\), \(\omega\), \(l\) and \(\theta\)?

• A. $\frac{m\omega L^2}{6}\sin 2\theta$
• B. $\frac{m\omega L^2}{3}\sin \theta$
• C. $\frac{m\omega L^2}{3}\sin \theta$
• D. $\frac{m\omega L^2}{3}\cos \theta$

Answer 1

The correct option is A $\frac{m\omega L^2}{6}\sin 2\theta$

Compute the angular momentum of each infinitesimal part by using $\overrightarrow{\alpha }=\overrightarrow{r}\times \overrightarrow{p}$