A conical pendulum consists of a plumb bob of mass m moving in a circular path in a horizontal plane, as shown in the figure to the right. During the movement, the support wire, of length l, maintains the constant angle θ with the vertical. Show that the magnitude of the angular momentum of the plumb bob about the center of the dotted circle is L = ((m ^ 2 gl ^ 3 sin ^ 4 θ) / cosθ) ^ (1⁄3).

A conical pendulum consists of a plumb bob of mass m moving in a circular path in a horizontal plane, as shown in the figure to the right. During the movement, the support wire, of length l, maintains the constant angle θ with the vertical. Show that the magnitude of the angular momentum of the plumb bob about the center of the dotted circle is L = ((m ^ 2 gl ^ 3 sin ^ 4 θ) / cosθ) ^ (1⁄3).