$A$ straight rod of length $L$ is released on a frictionless horizontal floor in a vertical position. As it falls and slips,the distance of a point on the rod from the lower end,which follows a quarter circular locus,is

$A$ rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time,when the rod makes an angle $\theta$ with the horizontal,the velocity of the $COM$ of the rod is $v_0$. The velocity of the end of the rod in contact with the surface at that instant is:

What is a rigid body? Explain the concept of a rigid body.

$A$ small particle of mass $m$ is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius $a$. All motion occurs essentially in the horizontal plane. If the angular velocity of the cord is $\omega_0$ when the distance from the particle to the tangency point is $r_0$,then the angular velocity of the cord $\omega$ after it has turned through an angle $\theta$ 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 direction of the angular velocity vector is along