Find the angular momentum of the system of at wood's machine used in example-5.4 after t second from start about point O, the axle ofpulley.

A body of mass m and radius r is released from rest along a smooth inclined plane of angle of inclination theta . The angular momentum of the body about the instantanoues point contact after a time t from the instant of release of equal is :

Three particles are moving as shown in the figure, Calculate the angular momentum of the third particle C , so that the angular momentum of system about point O becomes zero.

Suppose the rod with the balls A and B of theprevious problem is clamped at the centre in such a way that it ca rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a heigh h hon the ball B. The particle collides with B and sticks to it. a. Find the angular momentum and the angular speed of the system just after the collision. b. What should be the minimum value of h so that the system makes a full rotation after the collision.

A small ball of mass m suspended from the ceiling at a point O by a thread of length l moves along a horizontal circle with a constant angular velocity omega . Relative to which points does the angular momentum M of the ball remain constant? Find the magnitude of the increment of the vector of the ball's angular momentum relative to the point O picked up during half a revolution.

A certain system of particles possesses a total momentum p and an angular momentum M relative to a point O. Find its angular momentum M^' relative to a point O^' whose position with respect to the point O is determined by the radius vector r_0 . Find out when the angular momentum of the system of particles does not depend on the choice of the point O.

A wooden log of mass M and length L is hinged by a frictionless nail at O . A bullet of mass m strikes with velocity v and sticks to it. Find the angular velocity of the system, immediately after the collision about O . Also, calculate the minimum value of v so that log becomes horizontal after collision.

A disc A of mass m sliding over a smooth horizontal surface with velocity v experiences a perfectly elastic collision with a smooth stationary wall at a point O (figure). The angle between the motion direction of the disc and the normal of the wall is equal to alpha . Find: (a) the points relative to which the angular momentum M of the disc remains constant in this process, (b) the magnitude of the increment of the vector of the disc's angular momentum relative to the point O^' which is located in the plane of the disc's motion at the distance l from the point O.

A solid shere of mass m and radius R is kept over a rough ground. A time varying force F=2t is acting at the topmost point as shown in figure. (a). Find angular momentum of the sphere about the bottommost point as a function of time t (b). Does this result depend on the fact whether the ground is rough or smooth?

An uniform spherical shell of mass m and radius R starts from rest with pure rolling on long inclined plane as shown in figure. The angular momentum of shell about point of contact after 1 s of its starting is KmR. Determine the value of k(g=10m//s^(2)) .