How many degrees of freedom does a rigid body have for a rotational motion about a fixed axis?

$A$ 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

Explain the definitions of angular position,angular displacement,and angular speed for the motion of a rigid body.

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

$A$ homogeneous solid cylindrical roller of radius $R$ and mass $M$ is pulled on a cricket pitch by a horizontal force $F$ applied at its center. Assuming rolling without slipping,the angular acceleration of the cylinder is

$A$ rod of length $l$ and mass $m$ lies on a fixed horizontal smooth table. $A$ cord is led through a pulley,and its horizontal part is attached to one end of the rod,while its vertical part is attached to a block of mass $m_1$. Assume the pulley and the cord are ideal. The maximum possible acceleration of the rod's centre of mass $C$ (for all possible values of masses $m$ and $m_1$) at the moment of releasing the block $m_1$ is $\frac{g}{n}$. Find the value of $n$.