Serway & Jewett — Angular Momentum: Problem 12

Review. A conical pendulum consists of a bob of mass \( m \) in motion in a circular path in a horizontal plane as shown in Figure P11.12. During the motion, the supporting wire of length \( \ell \) maintains a constant angle \( \theta \) with the vertical. Show that the magnitude of the angular momentum of the bob about the vertical dashed line is \[ L = \left( \frac{m^2 g \ell^3 \sin^4 \theta}{\cos \theta} \right)^{1/2} \]