A small particle of mass on is projected with an initial velocity v at an angle 8 with x axis in X-Y plane as shown in Figure. Find the angular momentum of the particle.

A small particle of mass on is projected with an initial velocity v at

1.	A small particle of mass on is projected with an initial velocity v at an angle 8 with x axis in X-Y plane as shown in Figure. Find the angular momentum of the particle.
Answer» Solution :Let the particle of mass m cross a horizontal distance x in time t. ANGULAR momentum `vecL= int vec TAU dt` But `vectau= vecr xx vec F` `vecr=xhati+yhatj and vecF=-mg hatj` `:. Tau=(x hati+y hatj)xx(hati xx hatj)=-mgx hatk` `vecL=-mg int (x dt) hatk=- mgv cos theta( intdt) hatk)` Let INITIAL time =0 and final time `t=t_(1)` `:. vecL= mgv cos theta( underset(0) OVERSET(t_(f)) int t dt) hatk=-(1)/(2) mgv cos theta t_(f)^(2) hatk` Negative SIGN indicates, `vecL` point inwards