$A$ dancer is standing on a rotating platform holding two spheres in her hands. If she drops the spheres to the ground,the dancer's...

$A$ thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane with angular velocity $\omega$ about an axis passing through its center and perpendicular to the plane. If another ring of the same size but mass $\frac{M}{4}$ is placed coaxially on the first ring,then the new angular velocity of the system is:

The angular momentum of a particle performing circular motion under a central force is constant because of .........

$A$ 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 '$O$'?

$A$ ring of mass $M$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{M}{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant,the angular speed of the system is $\frac{8}{9} \omega$ and one of the masses is at a distance of $\frac{3}{5} R$ from $O$. At this instant,the distance of the other mass from $O$ is

Consider a uniform rod of mass $M=4m$ and length $\ell$ pivoted about its centre. $A$ mass $m$ moving with velocity $v$ making an angle $\theta=\frac{\pi}{4}$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is