# A pendulum swings through an angle of 48°. The pendulum is 45 inches long. How far does the end (or tip) of the pendulum travel in one pass?

Jan 31, 2017

$37.70$ inches

#### Explanation:

We begin by assuming that the pendulum can be considered to be a point mass. The length of a pendulum is usually measured to its center of mass. We will presume that the end, tip, and center of mass are at the same place.

Let's also assume that the instructions are suggesting that the pendulum swings 24º forward and 24º backwards in a complete cycle.

48 degrees is $\frac{48}{360}$ of a circle. The circumference of a circle of radius 45 inches is:
$C = 2 \pi r$
$C = 2 \pi \cdot 45 = 282.74$

The swing of the pendulum will be:
$\frac{48}{360} \cdot C = \frac{48}{360} \cdot 282.74 = 37.70 \text{ inches}$