$A$ body of mass $2 \ kg$ is moving in a circular path of radius $2 \ m$ with uniform speed. If the centripetal force acting on it is $100 \ N$,then its angular momentum is ....... $J \cdot s$.

When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign to $-\vec{r}$, which one of the following vectors will not flip its sign?

Define angular momentum.

If a particle of mass $m$ is moving with constant velocity $v$ parallel to the $X$-axis in the $x-y$ plane as shown in the figure,its angular momentum with respect to the origin at any time $t$ will be:

The Earth is assumed to be a sphere of radius $R$ and mass $M$ having a period of rotation $T$. The angular momentum of the Earth about its axis of rotation is

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side $a$ in free space. At $t = 0$,they are given an initial velocity $\vec{V}_A = V_0 \hat{u}_{AC}, \vec{V}_B = V_0 \hat{u}_{BA}$ and $\vec{V}_C = V_0 \hat{u}_{CB}$. Here,$\hat{u}_{AC}, \hat{u}_{CB}$ and $\hat{u}_{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally,then the magnitude of the net angular momentum of the system about the centroid of the triangle is: