$A$ spool of mass $M$ and radius $R$ is unwinding under gravity as a string is pulled. What is the acceleration of the spool?

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

$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

$A$ ring of mass $m$ can freely slide along the massless curved rod as shown. At the lower most point,the curved path becomes vertical. If the whole system is released from rest,what is the velocity of the ring $(v)$ at the lowermost point just before touching the block $M$ (all surfaces are smooth)?

$A$ 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

$A$ cord is wound round the circumference of a wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is $I$. $A$ weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$,the angular velocity of the wheel will be