Angular Impulse

A cylinder having moment of inertia, which is free to rotate about its axis, receives an angular impulse of J kgm^(2)//s initially, followed by similar impulse after every 4 s . What is the angular speed of the cylinder 30 s after the initial impulse?

A solid sphere (initially at rest) of mass 7 kg and radius 40 cm which is free to rotate about its axis is given an angular impulse of 5kgm^(2)s^(-1) followed by the similar impulse after every 5 second. Calculate the angular speed of sphere 50 s after the initial impulse.

A wheel of mass 2 kg and radius 20 cm initially at rest is free to rotate about its axis. It receives an angular impulse of 4kgm^(2)s^(-1) initially and similar impulse after every 5 s of initial one. Calculate the angular speed of the wheel 22 s after the initial impulse.

A cylinder of mass 5 kg and radius 30 cm and free to rotate about its axis receives an angular impulse of 3 kg m^(2) s^(-1) initially, followed by a similar impulse after every 4 second. What is the angular speed of the cylinder 30 s after the initial impulse ? The cylinder is at rest initially.

A solid sphere is rolling without slipping on rough ground as shown in figure. It collides elastically with another identical sphere at rest. There is no friction between the two spheres. Radius of each sphere is R and mass is m. What is the net angular impulse about centre of mass imparted to second sphere by the external forces?

Two cylinders with radii r_(1) and r_(2) and rotational inertia I_(1) and I_(2) are supported on their horizontal axles. The first one is set in rotation with angular velocity epsilon . The axle of the other cylinder (smaller) is moved until it touches the large cylinder and is caused to rotate by the frictional forces between the two. Find the angualr velocity of the two cylinders after slipping ceases between them. [Hint: Consider angular impulse received by the cylinders]

A thin plate of mass M ,length L and width 2d is mounted vertically on a frictionless fixed axle along the z -axis as shown. Initially, the object is at rest. it is then tapped with a hammer to provide a torque tau , which produces an angular impulse H about the z-axis of magnitude H = int tau dt . What is the angular speed co of the plate about the z -axis after the tap?

A clutch assembly consists of two discs A and B of moment of inertia 2I and I respectively, one being the engine fly wheel, the other one is the clutch plate. The discs are initially rotaing with angular velocities omega_(A)=omega and omega_(B)=2omega as shown in fig. When the two disc are brought into contact the discs rub against each other and eventually reach a common angualr velocity omega . (a) Derive an expressio for omega (b) What is the angular impulse of friction on any one of the discs?

A straight rigid rod of mass M and length L lies on a smooth horizontal table. Taking the co-ordinate axes as shown in the figure and assuming an average force ltFgt acting for a small time interval (/_\t) , at the end A , making an angle 30^@ with the X -axis, Based on the above passege, answer the following questions. The angular impulse, due to the force about O , is