Arc length

Definition

Arc length is the distance along a curved path of a circle or any curve. It can be calculated using the central angle in radians and the radius of the circle.

5 Must Know Facts For Your Next Test

1. Arc length, $s$, is given by the formula $s = r\theta$ where $r$ is the radius and $\theta$ is the central angle in radians.
2. Arc length is directly proportional to both the radius of the circle and the central angle.
3. To convert an angle from degrees to radians, use $\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}$.
4. In uniform circular motion, arc length can represent the distance traveled by an object along its circular path over a certain period.
5. If you know the circumference of a circle, you can find arc length as a fraction of this circumference based on the angle subtended at the center.

Review Questions

• What is the formula for calculating arc length?
• How does changing the radius of a circle affect its arc length?
• Convert an angle of 90 degrees into radians and calculate its corresponding arc length for a circle with a radius of 2 meters.

Related terms

Central Angle: An angle whose vertex is at the center of a circle and whose sides are radii intersecting the circle.

Radians:

A unit of measure for angles where one radian equals approximately 57.3 degrees; it represents an angle subtended by an arc equal in length to the radius.

Uniform Circular Motion:

Motion in which an object moves at constant speed along a circular path.