A ring of radius `r` made of wire of density `rho` is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in the figure. Determine the angular velocity (in rad/s) of ring at which the ring breaks. The wire breaks at tensile stress `sigma`. Ignore gravity. Take `sigma//rho = 4` and `r= 1 m.`

Radius of gyration of a ring of radius R about an axis passing through its centre and perpendicular to its plane is

Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is

Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is

A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity omega . Its kinetic energy is

A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity omega . Its kinetic energy is

A circular ring of radius R and mass m made of a uniform wire of cross sectional area A is rotated about a stationary vertical axis passing throgh its centre and perpendicular to the plane of the ring. If the breaking stress of the material of the ring is sigma_(b) , then determine the maximum angular speed omega_("max") at which the ring may be rotated without failure.