Question

Question #eae36

Answer 1

The acceleration is `a=gsintheta`

Explanation:

The forces acting on the pendulum will be `vecF_g` and `vecT`, this second being the tension in the cord.

As the diagram shows, we can resolve `vecF_g` into two components, namely `mgsintheta` and `mgcostheta`.

Because the rope does not stretch, it must be that `T=mgcostheta`, and these forces cancel.

Therefore, the net force acting on the pendulum is the "restoring force", `mgsintheta`

From Newton's second law

`F_"net" = mgsintheta`

`ma = mgsintheta`

and finally,

`a=gsintheta`

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

`alpha=a/L`

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

`alpha=g/L sintheta`