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.
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Let P1 and P2 are the position vectors of each particle.
also L1 , L2 and r1 ,r2 are the angular momenta And position vectors of the particles at the instant about any arbitrary point O.
angular momentum of particles,
L1 = r1×mv and L2 = r2× mv
Resultant of angular momentum (L) = L1 + L2
= r1×mv + r2mv
Because both are in opposite directions.
L = r1×mv +r2×m(-v)
|L|= r1mvsin∅1 - r2mvsin∅2
= mv{ r1sin∅1 - r2sin∅2}
See the figure ,
OM - ON = d
r1sin∅1 - r2sin∅2 = d
|L| = mvd
Hence, angular momentum of the two partlicle system is the same , whatever be the point about which the angular momentum is taken .
also L1 , L2 and r1 ,r2 are the angular momenta And position vectors of the particles at the instant about any arbitrary point O.
angular momentum of particles,
L1 = r1×mv and L2 = r2× mv
Resultant of angular momentum (L) = L1 + L2
= r1×mv + r2mv
Because both are in opposite directions.
L = r1×mv +r2×m(-v)
|L|= r1mvsin∅1 - r2mvsin∅2
= mv{ r1sin∅1 - r2sin∅2}
See the figure ,
OM - ON = d
r1sin∅1 - r2sin∅2 = d
|L| = mvd
Hence, angular momentum of the two partlicle system is the same , whatever be the point about which the angular momentum is taken .
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