The cirtical angular velocity `omega_c` of a cylinder inside another cylinder containing a liquied at which its turbulance occurs depends on visocisity `eta` density `rho` and disntac d between wall of the cylinder. Obtain an expression for `omega_c` using method of dimensios.

The critical angular velocity omega_c of a cylinder inside another cylinder containing a liquid at which its turbulence occurs depends on viscosity eta , density rho and the distance d between the walls of the cylinders . Find an expression for omega_c .

A gas fills up the space between two long coaxial cylinders of radii R_1 and R_2 , with R_1 lt R_2 . The outer cylinder rotates with a fairly low angular velocity omega about the stationary inner cylinder. The moment of friction forces acting on a unit length of the inner cylinder is equal to N_1 . Find the viscosity coefficient eta of the gas taking into account that the friction force acting on a unit area of the cylindrical surface of radius r is determined by the formule sigma = eta r(del omega//del r) .

An infinite cylinder of radius r with surface charge density sigma is rotated about its central axis with angular speed omega . Then the magnetic field at any point inside the cylinder is

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.

A string is wrapped around a cylinder of mass M and radius r. The string is pulled vertically upward to prevent the center of mass from falling as the cylinder unwinds the string. (a) What is the tension in the string? B) How much work has been done on the cylinder once it has reached an angular speed omega ? c) what is the length of string unwound in the time its acquires angular speed omega ?

A metal rod OA of mann 'm' and length 'r' is kept rotating with a constantangular speed omega in a vertical plane about a horizontal axis at the end O. The free end A is arraged to slide without friction along fixed conduction circular ring in the same plane as that of rotation. A uniform and constant magnetic induction vec(B) is applied perpendicular and into the plane of rotation as shown in the figure below. An inductor L and an external resistance R are connected through a swithch S between the point O and a point C on the ring to form an electrical circuit. Neglect the resistance of the ring and the rod. Initially, the switch is open. (a) What is the induced emf across the teminal of the switch? (b) The switch S is closed at time t=0. (i) Obtain an expression for the current as a function of time. (ii) In the steady state, obtin the time dependence of the torque required to maintain the constant angular speed, given that the rod OA was along th positive X-axis at t=0.

A cylinder rotating with angular velocity omega_(0) is put on a rough horizontal floor so that edge touches a vertical rough wall. Rotational motion of the cylinder is retarded and after some time cylinder comes to rest. If m is mass of cylinder and R is its radius then calculate number of revolutions made by the cylinder before it comes to rest. Assume mu is coefficient of friction for floor as well as wall.

A uniform solid cylinder of mass m and radius R is set in rotation about its axis with an angular velocity omega_(0) , then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and the plane is equal to mu . Find ( a ) how long the cylinder will move with sliding, ( b ) the total work performed by the sliding friction force acting on the cylinder.

A person stands in contact against the inner surface of a cylindrical drum of radius (R ) rotating with angular velocity omega . The coefficient of friction between the inner surface of the minumum rotational speed of the cylinder , which enables the person to ramain stuck to the wall , when the platform on which the person was standing is suddenly removed ?