$A$ cube of side '$a$' moves with a velocity '$v$' on a horizontal surface as shown in the figure. It hits an edge at point '$O$'. What will be the angular speed of the block after it hits point '$O$'?

$A$ solid sphere is rotating in free space. If the radius of the sphere is increased while keeping its mass constant,which of the following will $NOT$ be affected?

When a dancer pulls their arms inward while spinning on ice,they spin faster. This is due to:

$A$ circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two particles of mass $M$ are gently attached to the ring at the ends of a diameter. The ring will now rotate with an angular velocity $\omega'$ equal to:

$A$ circular disc of moment of inertia $I_t$ is rotating in a horizontal plane about its symmetry axis with a constant angular speed $\omega_i$. Another disc of moment of inertia $I_b$ is dropped coaxially onto the rotating disc. Initially,the second disc has zero angular speed. Eventually,both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is:

In a playground,there is a merry-go-round of mass $120\ kg$ and radius $4\ m$. The radius of gyration is $3\ m$. $A$ child of mass $30\ kg$ runs at a speed of $5\ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.