A particle is moving along a stright line parallel to x-axis with constant velocity. Does its angular momentum about the origin decrease with time or increase with time or remain constant ?

Explanation

Suppose a particle of mass `m` is moving II to X-axis starting from `B`, where `OB = b`, Fig. At any time `t`, let the particle be at `P`,
where `x = OA = BP = v t, y = b, z = 0`.
Components of velocity are

`v_(x) = (dx)/(dt) =v, v_(y) = (dy)/(dt) = 0, v_(Z) = 0`
As `overset rarr(L) = overset rarr(r ) xx overset rarr(P) = overset rarr(r ) xx m overset rarr(v) = m(overset rarr(r ) xx overset rarr(v))`
`= m|[hati,hatj,hatk],[vt,b,0],[v,0,0]|`
i.e. angular momentum has magnitude `m v b` and is directed along negative z-axis. Thus angular momentum remains constant.