Two particles, each of mass m and moving with speed v in...

Two particles, each of mass $m$ and moving with speed $v$ in opposite directions along parallel lines are separated by a distance $d$. The vector angular momentum of this system of the particles will be : (a) maximum when the origin is taken beyond the two parallel lines on either sides (b) maximum when the origin is taken beyond the two parallel lines on either sides (c) maximum when the origin is taken beyond the two parallel lines on either sides (d) same, no point is taken as the origin

Two particles, each of mass $m$ and moving with speed $v$ in opposite directions along parallel lines are separated by a distance $d$. The vector angular momentum of this system of the particles will be :
(a) maximum when the origin is taken beyond the two parallel lines on either sides
(b) maximum when the origin is taken beyond the two parallel lines on either sides
(c) maximum when the origin is taken beyond the two parallel lines on either sides
(d) same, no point is taken as the origin

Key Concepts

Angular Momentum

Angular momentum is defined as the cross product of a particle’s position vector and its linear momentum. It characterizes the rotational effect of a force about a point and is fundamentally linked to the concept of rotation in mechanics.

Reference Point Dependence

The angular momentum of a single particle depends on the choice of the origin because the position vector is measured relative to that point. However, when considering a system of particles, if the net (total) linear momentum is zero, shifting the origin does not change the total angular momentum of the system, as the additional contributions cancel each other out.

Total Angular Momentum of a System

The total angular momentum of a system is the vector sum of the angular momenta of all individual particles. For a system with balanced (or canceling) linear momenta, such as equal and opposite moving particles, the overall angular momentum remains invariant under a change of origin.

Invariance Under Translation in Zero Net Momentum Systems

For systems where the sum of the particles' momenta equals zero, the angular momentum calculated about any point remains the same. This invariance arises because any shift in the origin introduces an extra term proportional to the total linear momentum, which is zero in this case, thereby leaving the angular momentum unchanged.

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