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

$A$ cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. $A$ rope of negligible mass is wrapped around the cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

$A$ solid sphere of radius $R$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at a height $h$ from the lowest point. For the maximum acceleration of the centre of mass,which is correct?

What is a rigid body?

$A$ uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). $A$ massless string is wrapped over its rim and two blocks of masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_{1}$ descends by a distance $h$ is

The spool shown in the figure is placed on a rough horizontal surface and has an inner radius $r$ and an outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $\theta$ for which the spool does not roll and remains stationary is given by: