Arc Length Math Example 4

Follow the full solution, then compare it with the other examples linked below.

hard

A pendulum of length

80

cm swings through an angle of

0.4

radians. How far does the tip of the pendulum travel in one complete swing (from one side to the other and back)?

1
Step 1: The arc length for one side of the swing (one-way) is $s = r\theta = 80 \times 0.4 = 32$ cm.
2
Step 2: A complete swing goes from one extreme to the other (one-way) and back, covering the arc twice: total distance $= 2 \times 32 = 64$ cm.

Answer

64

Using

s = r\theta

, the pendulum tip traces an arc of

80 \times 0.4 = 32

cm in each direction. A full swing (out and back) covers

2 \times 32 = 64

cm. This is a real-world application of arc length with radians.

About Arc Length

The distance along a portion of a circle's circumference, determined by the central angle and the radius.

A circle has radius [formula] cm. Find the arc length intercepted by a central angle of [formula].

A circle has radius [formula] m. Find the arc length subtended by a central angle of [formula] radia

A circle has a radius of [formula] cm. What is the arc length for a central angle of [formula]?