What is the linear velocity if angular velocity $\vec{\omega} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$?

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be

$A$ string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to the ceiling. The centre of mass falls down as the disc unwinds the string. The tension in the string is

$A$ thin rod is hinged at point $O$ and is in an unstable equilibrium position. It falls under the influence of gravity due to a slight disturbance. It makes angles of $60^{\circ}$,$90^{\circ}$,and $180^{\circ}$ with the vertical in positions $(2)$,$(3)$,and $(4)$ respectively. If $\omega_2$,$\omega_3$,and $\omega_4$ are the angular velocities in these positions,then:

$A$ body is in pure rotation. The linear speed $v$ of a particle,the distance $r$ of the particle from the axis,and the angular velocity $\omega$ of the body are related as $\omega = \frac{v}{r}$. Thus,

What is rotational motion and an axis of rotation?