A particle of mass m moves in the xy-plane with velocity of `vec v = v_x hat i+ v_y hat j`. When its position vector is `vec r = x vec i + y vec j`, the angular momentum of the particle about the origin is.

Options

A. `m(xv_y + yv_x) hat k`
B. `-m(xv_y + yv_x) hat k`
C. `m(yv_x - xv_y) hat k`
D. `m(xv_y - yv_x) hat k`.

Answer

D

Explanation

(d) We use `vec L = vec r xx vec p` :
`vec L = |{:(hati,hatj,hatk),(x,y,0),(mv_(x),mv_(y),0):}|`
=`hat i(0 - 0) - hat j (0 - 0) + hat k(mxv_y - myv_x)`
`vec L = m(xv_y - yv_x) hat k`.