"In pure translation motion velocity of every particle of body at any instant" is what? Equal or unequal ?

Obtain Newton's second law for system of particle and write it. 

In rotational motion of a rigid body, all particle move with

For the given figure find the acceleration of $1\, kg$ block if string is massless and mass of the pulley is $2\, kg$ and diameter of puller is $0.2\, m$ (in $m / s ^{2}$)

A solid sphere rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of sphere, then passes through over a solid cylinder and then is connected to block of mass $M$ as  shown in figure. If the system is released from rest then the speed acquired by block after it has fallen through distance $h$ is

Let $\mathop A\limits^ \to  $ be a unit vector along the axis of rotation of a purely rotating body and $\mathop B\limits^ \to  $ be a unit vector along the velocity of a particle $ P$ of the body away from the axis. The value of $\mathop A\limits^ \to  .\mathop B\limits^ \to  $ is