In amusement parks there is a device called rotor where people stand on a platform inside a large cylinder that rotates about a vertical axis. When the rotor reaches a certain angular velocity, the platform drops away. Find the minimum coefficient of friction for the people not to a slide down. Take the radius to be `2m` and the period to be `2s`.

An insect of mass m=3kg is inside a vertical drum of radius 2m that is rotating with an angular velocity of 5rads^(-1) . The insect doesn't fall off. Then, the minimum coefficient of friction required is

A hollow vertical cylinder of radius R is rotated with angular velocity omega about an axis through its centre. What is the minimum coefficient of static friction between block M and cylinder wall necessary to keep the block suspended on the inside of the cylinder ?

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad s^(-1) . The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip. (Take g = 10 m//s^(2) )

Two block of masses m and M are connected by a chord passing around a frictionless pulley which is attached to a rotating frame , which rotates about a vertical axis with an angular velocity omega If the coefficient of friction between the two masses and the surface are mu_(1) and mu_(2) respectively determine the value of omega at which the block starts sliding radially (M gt m)

A uniform rod AB of length 2l and mass m is rotating in a horizontal plane about a vertical axis through A, with angular velocity omega , when the mid-point of the rod strikes a fixed nail and is brought immediately to rest. Find the impulse exerted by the nail.

An inclined plane of angule a is fixed onto a horizontal turntable with its line of greater slope in same plane as a diameter of forntable .A small block is placed on the inclined plane a distance r from the axis the coefficient of fraction between the block and the inclined plane is mu The turntable along with incline plane spins about its axis with constant minimum angular velocity omega a. Find an capression for the minimum angular velocity omega to prevent the block from sliding down the plane in term of g, r, mu and the plane omega b. Now a block of mass but having coefficient friction (with inclined plane) 2mu is kept instead of the original block . find the radius of friction force acting between block and incline now to the friction force active in part (a)

A child of mass m is standing, on the periphery of a circular platform of radius R , which can rotate about its central axis. The moment of inertia of the platform is I . Child jumps off from the platform with a velocity u tangentially relative to the platform. Find the angular speed of the platform after the child jumps off.

A disc of radius R rotates from rest about a vertical axis with a constant angular acceleration such that a coin placed with a tangenitial between a as shown in figure If the coefficient of static friction between the coin and disc is mu_(s) .Find the velocity of the before it start sliding relative as the disc

A block of mass 1kg is placed on the periphery of a rotating rough circular table of radius 50cm as shown in the figure.Angular velocity of the table is 4 rad/s.The minimum value of coefficient of friction between the contact such that there is no relative slipping is (g= 10 m/s^2)

A small bead of mass m = 1 kg is free to move on a circular hoop. The circular hoop has centre at C and radius r = 1 m and it rotates about a fixed vertical axis. The coefficient of friction between bead and hoop is mu=0.5 . The maximum angular speed of the hoop for which the bead does not have relative motion with respect to hoop, at the position shown in figure is : (Take g = 10 m//s^(2) )