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Home » Two particles, each of mass and speed v, travel in opposite directions along parallel lines separated by a distance . 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 angular momentum vector of the two-particle system is the same whatever be the point about which the angular momentum is taken
CBSE | Class 11 | NCERT | Physics | System of Particles and Rotational Motion
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

Considering three points Z, C and X :

Angular momentum at Z will be given as,

\mathrm{Lz}=\mathrm{mv} \times 0+\mathrm{mv} \times \mathrm{d}

=\mathrm{mvd}-(1)

Angular momentum about x will be given as

\mathrm{L}_{x}=m v \times d+m v \times 0

=\mathrm{mvd}-(2)

Angular momentum about C will be given as

L_{c}=m v x y+m v x(d-y)=m v d-(3)

As a result, we can infer,

\mathrm{L}_{\mathrm{z}}=\mathrm{L}_{\mathrm{x}}=\mathrm{L}_{\mathrm{c}}

The above solution proves that the angular momentum of a system does not depend on the point about which its taken.

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