The position vectors of two points are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$,and the linear momentum is $2\hat i + 3\hat j - \hat k$. The angular momentum is:

$A$ mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is $L$. If the length of the string is now halved, keeping the angular velocity the same, then the angular momentum will be:

$A$ thin uniform rod of length $L$ and mass $m$ is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$. If a horizontal impulse $P$ is imparted to the rod at a distance $x = L/n$ from the mid-point of the rod (see figure), then the rod and string revolve together around the point $O$, with the rod remaining aligned with the string. In such a case, the value of $n$ is:

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

Write the $SI$ unit of angular momentum and its dimensional formula.

$A$ particle is rotating in a circle with uniform speed as shown. The angular momentum of the particle with respect to the origin is .........