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.

Explanation

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( int dt) 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