1. ## Arc Length

Just a quick question.

Is the arc length $\displaystyle L$ of a circle with radius $\displaystyle r$, made by the angle $\displaystyle \theta$, $\displaystyle L = r \theta$ or $\displaystyle L = 2r \theta$?

Measuring $\displaystyle \theta$ in radians obviously.

Thanks

2. Originally Posted by craig
Just a quick question.

Is the arc length $\displaystyle L$ of a circle with radius $\displaystyle r$, made by the angle $\displaystyle \theta$, $\displaystyle L = r \theta$ or $\displaystyle L = 2r \theta$?

Measuring $\displaystyle \theta$ in radians obviously.

Thanks
When the radius vector completes one rotaτion, it covers an angle 2π radians. The tip of the vector moves through a distance 2πr.
So when the distance moved by tip is L, what the angle covered by the vector?

3. Originally Posted by craig
Just a quick question.

Is the arc length $\displaystyle L$ of a circle with radius $\displaystyle r$, made by the angle $\displaystyle \theta$, $\displaystyle L = r \theta$ or $\displaystyle L = 2r \theta$?

Measuring $\displaystyle \theta$ in radians obviously.

Thanks
Which one gives the correct circumference ($\displaystyle \theta = 2 \pi$) ....?

4. Thanks for the replies, not sure what happened then, just couldn't visualise it at all

Arc length $\displaystyle L = r \theta$

Cheers for that