In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. If there is no slipping,find its angular acceleration $\alpha_2$.

$A$ 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)?

What is pure translational motion?

$A$ uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. $A$ string is wrapped over its rim and a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

$A$ uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed $\omega$ about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis,then which of the following graphs depicts it most closely?

$A$ rigid body is rotating with variable angular velocity $\omega = (a - bt)$ at any instant of time $t$. The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants).