Let $\vec{A}$ be a unit vector along the axis of rotation of a purely rotating body and $\vec{B}$ be a unit vector along the velocity of a particle $P$ of the body away from the axis. The value of $\vec{A} \cdot \vec{B}$ is

Between the hour hand of a clock and the rotation of the Earth about its own axis,which has a lower angular speed?

$A$ ball of mass $m$ is released from inside a smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$?

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

$A$ string is wrapped around a cylinder of radius $r$ and moment of inertia $I$. $A$ mass $m$ is attached to one end of the string. The cylinder can rotate freely about its horizontal axis. If the mass $m$ is released from rest at a height $h$,what will be its velocity?

$A$ uniform disc with mass $M = 4\,kg$ and radius $R = 10\,cm$ is mounted on a fixed horizontal axle as shown in the figure. $A$ block with mass $m = 2\,kg$ hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block,the cord does not slip and there is no friction at the axle. The tension in the cord is . . . . . . $N$. (Take $g = 10\,m/s^2$)