Two particles each of mass `m` and speed `v`, travel in opposite direction along parallel lines separated by a distance d. Show that the vector angular momentum of this system of particles is the same about any point taken as origin.

Two particles of masses m_1 and m_2 are joined by a light rigid rod of length r. The system rotates at an angular speed omega about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is L=mur^2omega where mu is the reduced mass of the system defined as mu=(m_1m_2)/(m_1+m_2)

Two parallel wires carry equal currents of 10A along the same direction and are separated by a distance of 2.0 cm. Find the magnetic field at a point which is 2.0 cm away from each of these wires.

Two ball bearing of mass m each moving in opposite directions with equal speeds v collide head on with each other. Predict the outcome of the collision, assuming it to be perfectly elastic.

A particle of mass 5 units is moving with a uniform speed of v = 3 sqrt(2) units in the XOY plane along the line y = x + 4. Find the magnitude of angular momentum.