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.
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Arc length, $s$, is given by the formula $s = r\theta$ where $r$ is the radius and $\theta$ is the central angle in radians.
Arc length is directly proportional to both the radius of the circle and the central angle.
To convert an angle from degrees to radians, use $\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}$.
In uniform circular motion, arc length can represent the distance traveled by an object along its circular path over a certain period.
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.