The angular momentum of a flywheel having a moment of inertia of $0.4\, kg\, m^2$ decreases from $30\, kg\, m^2/s$ to $20\, kg\, m^2/s$ in a period of $2\, s$. The average torque acting on the flywheel during this period is ......... $N\, m$.

The angular momentum of a system of particles changes if:

$A$ small particle of mass $m$ is projected at an angle $\theta$ with the $x$-axis with an initial velocity $v_0$ in the $x-y$ plane as shown in the figure. At a time $t < \frac{v_0 \sin \theta}{g}$,the angular momentum of the particle is

$A$ 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:

$A$ particle of mass $m$ moves along a straight line $AB$ in the $XY$ plane. Let $L_A$ and $L_B$ be the angular momentum of the particle about the origin $O$ when it is at points $A$ and $B$ respectively. Then:

When a particle is moving in a circular path around a fixed point in a plane,the direction of its angular momentum is ........