Radians

Definition

Radians are a unit of angular measure used in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc whose length is equal to the circle's radius.

5 Must Know Facts For Your Next Test

1. There are $2\pi$ radians in a full circle or $360^\circ$.
2. Radians provide a direct relationship between the arc length and radius, making calculations in circular motion more straightforward.
3. In equations involving angular velocity, radians per second ($rad/s$) is the standard unit.
4. Radians are dimensionless units, often simplifying mathematical expressions in physics.
5. The conversion from degrees to radians is given by multiplying degrees by $\frac{\pi}{180}$.

Review Questions

• How many radians are there in a full circle?
• What is the relationship between arc length, radius, and radians?
• Convert $90^\circ$ to radians.

Related terms

Angular Velocity: The rate of change of the rotation angle per unit time, typically measured in radians per second ($rad/s$).

Arc Length: The distance along the curved path of a circle; it can be calculated using $s = r \theta$, where $s$ is the arc length, $r$ is the radius, and $\theta$ is the angle in radians.

Rotation Angle: The angle through which an object rotates around a fixed axis; it can be measured in degrees or radians.