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 ......... $N\, m$.

In orbital motion,the angular momentum vector is directed:

$A$ cylinder of mass $5 \ kg$ and radius $30 \ cm$ is free to rotate about its axis. It receives an initial angular impulse of $3 \ kg \ m^2 s^{-1}$ and subsequently receives the same impulse every $4 \ s$. What will be the angular speed of the cylinder $30 \ s$ after the initial impulse? The cylinder is initially at rest.

Explain the angular momentum of a particle and show that it is the moment of linear momentum about the reference point.

Two wheels are connected by a belt. The radius of the larger wheel is three times that of the smaller one. What is the ratio of the rotational inertia of the larger wheel to the smaller wheel,when both wheels have the same angular momentum?

$A$ particle of mass $2\, kg$ is moving such that at time $t$,its position,in meters,is given by $\vec{r}(t) = 5\hat{i} - 2t^2\hat{j}$. The angular momentum of the particle at $t = 2\, s$ about the origin in $kg\, m^2\, s^{-1}$ is: