For the given figure,find the acceleration of the $1\, kg$ block. The string is massless,the mass of the pulley is $M = 2\, kg$,and the diameter of the pulley is $0.2\, m$. (in $m/s^2$)

Two small balls are fixed at the ends of a light rigid rod of length $L = 0.4 \ m$. The system is released from a height $h = 5 \ m$ with the rod horizontal. The balls collide with the horizontal surface and rebound. The coefficient of restitution between ball $A$ and the ground is $e_A = 0.6$ and that between ball $B$ and the ground is $e_B = 0.4$. Find the angular speed (in $rad/s$) of the rod just after the collision. Take the acceleration due to gravity $g = 10 \ m/s^2$.

$A$ rigid lamina is rotating about an axis passing perpendicular to its plane through point $O$ as shown in the figure. The angular velocity of point $B$ with respect to $A$ is ....... $rad/s$.

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 $\vec{v}$?

What is the direction of angular velocity in circular motion about a fixed axis of rotation?

For a rigid body in rotational motion,if the linear velocity of a particle at a distance of $2 \ cm$ from the fixed axis of rotation is $10 \ cm \ s^{-1}$,what is the angular velocity of a particle at a distance of $4 \ cm$ from the axis of rotation?