# Question #eae36

Feb 20, 2017

The acceleration is $a = g \sin \theta$

#### Explanation:

The forces acting on the pendulum will be ${\vec{F}}_{g}$ and $\vec{T}$, this second being the tension in the cord.

As the diagram shows, we can resolve ${\vec{F}}_{g}$ into two components, namely $m g \sin \theta$ and $m g \cos \theta$.

Because the rope does not stretch, it must be that $T = m g \cos \theta$, and these forces cancel.

Therefore, the net force acting on the pendulum is the "restoring force", $m g \sin \theta$

${F}_{\text{net}} = m g \sin \theta$

$m a = m g \sin \theta$

and finally,

$a = g \sin \theta$

If you prefer, you can express the acceleration as an angular acceleration:

$\alpha = \frac{a}{L}$

in which case the angular acceleration of the pendulum bob, moving in a circular arc, is

$\alpha = \frac{g}{L} \sin \theta$