The rate of chage of angular momentum = the net torque on the object.
The net torque is the weight "mg" times the perpendicular distance from the line of action of the weight to the origin, x
dL/dt = mgx = mgrCos(36.8)
Or it is the component of the weight perpendicular to the position vector, mgCos(36.8) , times the magnitude of the position vector, r ;
dL/dt = {mgCos(36.8}]r
Obviously the same eq.
Everything is given, so just plug in the values. The particle velocity is not needed to find rate of change of L.