A-particle-of-mass-m-is-moving-in-yz-plane-with-a-uniform-velocity-v-with-its-trajectory-running-parallel-to-ve-y-axis-and-intersecting-z-axis-at-z-a-The-change-in-its-angular-momentum-about-the-

Question Number 24786 by Tinkutara last updated on 26/Nov/17

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{in}\:{yz}-\mathrm{plane} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{velocity}\:{v}\:\mathrm{with}\:\mathrm{its} \\ $$$$\mathrm{trajectory}\:\mathrm{running}\:\mathrm{parallel}\:\mathrm{to}\:+\mathrm{ve}\:{y}- \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{intersecting}\:{z}-\mathrm{axis}\:\mathrm{at}\:{z}\:=\:{a}. \\ $$$$\mathrm{The}\:\mathrm{change}\:\mathrm{in}\:\mathrm{its}\:\mathrm{angular}\:\mathrm{momentum} \\ $$$$\mathrm{about}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{as}\:\mathrm{it}\:\mathrm{bounces}\:\mathrm{elastically} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{at}\:{y}\:=\:\mathrm{constant}\:\mathrm{is}\:: \\ $$$$\left(\mathrm{1}\right)\:{mva}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{mva}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{3}\right)\:{ymv}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{ymv}\overset{\wedge} {{e}}_{{x}} \\ $$

Commented by Tinkutara last updated on 26/Nov/17

Answered by ajfour last updated on 26/Nov/17

l^� =r^� ×p^� △l^� =r^� ×△p^� =(yj^� +ak^� )×(−2mvj^� ) =2mvai^� ≡ 2mvae_x ^� option (2).

$$\bar {{l}}=\bar {{r}}×\bar {{p}} \\ $$$$\bigtriangleup\bar {{l}}=\bar {{r}}×\bigtriangleup\bar {{p}} \\ $$$$\:\:\:\:\:\:=\left({y}\hat {{j}}+{a}\hat {{k}}\right)×\left(−\mathrm{2}{mv}\hat {{j}}\right) \\ $$$$\:\:\:\:\:\:=\mathrm{2}{mva}\hat {{i}}\:\:\equiv\:\mathrm{2}{mva}\hat {{e}}_{{x}} \\ $$$${option}\:\left(\mathrm{2}\right). \\ $$

Commented by Tinkutara last updated on 26/Nov/17