Chapter 4.8, Problem 7E

To determine

(a)

To prove:

The angular momentum of mass is given by $m{l}^2\frac{d\theta }{dt}$, where $m$ is pendulum mass, $l$ is lever arm’s length.

To determine

(b)

To prove:

That the torque produced by a mass $m$, arm length $l$ and the perpendicular component vector of gravitational force is given by $-lmg\sin \theta$.

To determine

(c)

To deduce:

The pendulum equation $m{l}^2{\theta }^{″}=-lmg\sin \theta$ by the use of Newton’s law of rotational motion.