A cylinder of mass M, radius `r_(1)` and lenglth l is kept inside another cylinder of radius `r_(2)` and length l. The space between them is filled with a liquid of viscosity `eta`. The inner cylinder starts rotating with angular velocity `omega` while the other cylinder is at rest. Find time when inner cylinder stops.

There are two concentric cylinders of radii R_(1) and R_(2) as shown. The narrow space between the two cylinders is filled with liquid of viscosity mu . The inner cylinder is held stationary by means of a torsional spring of stiffness G. the outer cylinder is rotated with constant angular speed omega . The torque acting on the inner cylinder due to shearing action of thhe liquid:

There are two concentric cylinders of radii R_(1) and R_(2) as shown. The narrow space between the two cylinders is filled with liquid of viscosity mu . The inner cylinder is held stationary by means of a torsional spring of stiffness G. the outer cylinder is rotated with constant angular speed omega . The torque acting on the inner cylinder due to shearing action of thhe liquid:

A long cylinder of radius R_1 is displaced along its axis with a constant velocity v_0 inside a stationary co-axial cylinder of radius R_2 . The space between the cylinders is filled with viscous liquid. Find the velocity of the liquid as a function of the distance r from the axis of the cylinders. The flow is laminar.

Two cylinders having radiii R_(1) and R_(2) and rotational inertia I_(1) and I_(2) respectively, are supported by fixed axes perpendicular to the plane of figure-5.52. The large cylinder is initially rotating with angular velocity omega_(0) . The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually, slipping ceases, and the two cylinders rotate at constant rates in opposite directions, (a) Find the final angular velocity omega_(2) of the small cylinder in terms of I_(1) , I_(2) , R_(1) , R_(2) and omega_(0) . (b) Is total angular momentum conserved in this case ?

What is moment of inertia of a solid cylinder of mass m , length l and radius r about the axis of the cylinder ?

Under standard conditions helium fills up the space between two long coaxial cylinders. The mean radius of the cylinders is equal to R , the gap between them is equal to Delta R , with Delta R lt lt R . The outer cylinder rotates with a fairly low angular velocity omega about the stationary inner cylinder. Down to what magnitude should the helium pressure be lowered (keeping the temperature constant) to decrease the sought moment of friction forces n = 10 times if Delta R = 6 mm ?

A solid cylinder has mass M ,length L and radius R.The moment of inertia of this cylinder abot a gerator is :