Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.

Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.

A particle of mass m is moving with constant speed v on the line y=b in positive x-direction. Find its angular momentum about origin, when position coordinates of the particle are (a, b).

Two particles each of mass m are connected by a light inextensible string and a particle of mass M is attached to the midpoint of the string. The system is at rest on a smooth horizontal table with string just taut and in a straight line. The particle M is given a velocity v along the table perpendicular to the string. Prove that when the two particles are about to collide : (i) The velocity of M is (Mv)/((M + 2m)) (ii) The speed of each of the other particles is ((sqrt2M (M + m))/((M + 2m)))v .

A particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line :

A particle of mass m has been thrown with intial speed u making angle theta with the horizontal ground. Find the angular momentum of the projectile about an axis perpendicular to the plane and passing through the point of projection when the projectile is (a) At the highest point (b) About to hit the ground

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s^(-1) collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?

Two particles A and B start at O travel in opposite directions along the circular path at constant speed v_(A)=0.7 m//s and v_(B)=1.5 m//s respectively. Determine the time when they collide and the magnitude of the acceleration of B just before this happening. ("radius"=5m)

Two particles execute SHM of same amplitude and frequency on parallel lines. They pass one another when moving in opposite directions each time their displacement is one third their amplitude. What is the phase difference between them?

Assertion:- In two particle system when viewed from center of mass reference frame, if one particle slops then other one will also stop simultaneously, irrespective of external forces acting on system. Reason:- Centre of mass of a system is a point about which total momentum of system is always constant and non-zero.