College Physics I – Introduction

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Radians

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College Physics I – Introduction

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.

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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.
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