A sleeve `A` can slide freely along a smooth rod bent in the shape of a half circle of radius `R` .The system is set in rotaion with a constant angular velocity `omega` about a vertical axis `OO'` .Find the angle `theta` corresponding to the steady position of the sleeve

A sleeve A can slide freely along a smooth rod bent in the shape of a half-circle of radius R(figure). The system is set in rotation with a constant angular velocity omega about a vertical axis OO^' . Find the angle theta corresponding to the steady position of the sleeve.

A smooth uniform rod of length L and mass M has two identical beads of negligible size each of mass m which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with an angular velocity omega_0 about an axis perpendicular to the rod and passing through the midpoint of the rod. There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is ......

A smooth uniform rod of length L and mass M has two identical beads of negligible size each of mass m which can slide freely along the rod. Initially the two beada are at the centre of the rod and the system is rotating with an angular velocity omega_0 about an axis perpenducular to the rod and passing through the midpoint of the rod. There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is ......

A rope of mass'm' is looped in a circle of radius R and rotated with a constant angular velocity about its axis in gravity free space . Find the tension in the rope ?

A chain of mass m forming a circle of radius R is slipped on a smooth round cone with half- angle theta . Find the tension in the chain if it rotates with a constant angular velocity omega about a vertical axis coinciding with the symmetry axis of the cone .

A chain of mass m forming a circle of radius R is slipped on a smooth round cone with half- angle theta . Find the tension in the chain if it rotates with a constant angular velocity omega about a vertical axis coinciding with the symmetry axis of the cone .

In the arrangement shown, the sleeve of mass M is fixed between two identical springs whose combined force constant is k . The sleeve can slide without friction over a horizontal bar AB . The arragement rotates with a constant angular velocity omega about a vertical axis passing through the middle of the bar. the period of small oscillations of teh sleeve is.........

In the arrangement shown in figure the sleeve M of mass m=0.20kg is fixed between two identical springs whose combined stiffness is equal to x=20 N//m . The sleeve can slide without friction over a horizontal bar AB . The arrrangement rotates with a constant angular velocity omega=4.4 rad//s about a vertical axis passing through the middle of the bar . Find the period of small oscillations of the sleeve. At what values of omega will there be no oscillations of the sleeve ?