$A$ ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along $\qquad$

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is

Write the formula expressing the relationship between linear velocity and angular velocity for a particle in rotational motion.

In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

Let $\vec{A}$ be a unit vector along the axis of rotation of a purely rotating body and $\vec{B}$ be a unit vector along the velocity of a particle $P$ of the body away from the axis. The value of $\vec{A} \cdot \vec{B}$ is

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?