What is the direction of angular velocity for a rigid body?

How can one verify that an object is undergoing rotation about a fixed axis?

$A$ truck is moving at a speed of $54 \ km/h$. The radius of its wheels is $50 \ cm$. If the wheels come to rest after $20$ rotations upon applying brakes,what is the linear distance covered by the truck during this time? What is the angular acceleration of the wheels?

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha - \beta t$,where $t$ is time and $\alpha, \beta$ are constants. Find the angle (in radians) through which it rotates before it stops.

As shown in the figure,a bob of mass $m$ is tied by a massless string whose other end portion is wound on a flywheel (disc) of radius $r$ and mass $m$. When released from rest,the bob starts falling vertically. When it has covered a distance of $h$,the angular speed of the wheel will be

Consider two masses with $m_1 > m_2$ connected by a light inextensible string that passes over a pulley of radius $R$ and moment of inertia $I$ about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance $2h$. When the two masses pass each other,the speed of the masses is proportional to