$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)

$A$ spool of mass $M$ and radius $R$ is unwinding under gravity as a string is pulled. What is the acceleration of the spool?

For a particle,the angular velocity is $\vec{\omega} = \hat{i} - 2\hat{j} + 3\hat{k}$ and the position vector is $\vec{r} = \hat{i} + \hat{j} + \hat{k}$. What is the linear velocity $\vec{v}$?

$A$ mass $m$ is suspended from a string wrapped around a frictionless pulley. The pulley has a mass $M$ and radius $R$. If the pulley is a uniform circular disk and the string does not slip on the pulley,what is the acceleration of the mass?

$A$ flywheel having mass $3 \ kg$ and radius $5 \ m$ is free to rotate about a horizontal axis. $A$ string having negligible mass is wound around the wheel and the loose end of the string is connected to a $3 \ kg$ mass. The mass is kept at rest initially and released. The kinetic energy of the flywheel when the mass descends by $3 \ m$ is . . . . . . $J$. $(g = 10 \ m/s^{2})$

Write the change in magnitude and direction of angular velocity with respect to time for a body rotating about a fixed axis.