$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

What are the characteristics of rotational motion?

$A$ ring of mass $m$ can freely slide along the massless curved rod as shown. At the lower most point,the curved path becomes vertical. If the whole system is released from rest,what is the velocity of the ring $(v)$ at the lowermost point just before touching the block $M$ (all surfaces are smooth)?

$A$ uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. $A$ string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

$A$ uniform disc of radius $R$ and mass $M$ can rotate on a smooth axis passing through its centre and perpendicular to its plane. $A$ force $F$ is applied on its rim as shown in the figure. What is the tangential acceleration of the rim?

The velocity of the centre of mass of a rigid rod with respect to an observer $O$ is $\vec v_{cm} = (2\hat i + 3\hat j) \text{ m/s}$. The rod has an angular velocity about its centre of mass given by $\vec \omega = (3\hat j + 4\hat k) \text{ rad/s}$. Let $A$ be a point on the rod with position vector $\vec r = 2(\hat i + \hat k) \text{ m}$ with respect to the centre of mass. The velocity of the point $A$ with respect to $O$ is: