$A$ particle moves in a circular path with decreasing speed. Choose the correct statement.

  • A
    Angular momentum remains constant
  • B
    Acceleration $(\vec a)$ is towards the center
  • C
    Particle moves in a spiral path with decreasing radius
  • D
    The direction of angular momentum remains constant

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Write the general formula of total angular momentum of rotational motion about a fixed axis.

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ are denoted by $\vec{L}_O$ and $\vec{L}_P$ respectively,then

$A$ thin rod of mass $M$ and length $L$ is struck at one end by a ball of clay of mass $m$,moving with speed $v$ as shown in the figure. The ball sticks to the rod. After the collision,the angular momentum of the clay-rod system about $A$,the midpoint of the rod,is:

Why is the angular momentum perpendicular to the axis,denoted as ${L_ \bot }$,zero in a rotational motion about a fixed axis?

The position vector of a particle is $\vec{r} = (\hat{i} + 2\hat{j} - \hat{k})$ and its momentum is $\vec{p} = (3\hat{i} + 4\hat{j} - 2\hat{k})$. The angular momentum of this particle is perpendicular to:

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