Question

What is the formula for the angle displacement of a circle, given its radius and arc-length traveled?

Ideas: I found w=s/r which is omega = arc length/radius
However, when I used that in a calculation, it failed.

Example: Radius is 133.4cm, Arc-length traveled is 12.2cm. Find the angle displacement.

Answer 1

Idea #2: w is measured in radians, so I guess I have to convert s and r to radians by finding the circumference of the circle, convert that to radians, and use that to find the arc length in radians, and the radius into radians as well.

Can anyone double-check to make sure my logic isn't trumped-up trickled down?

Answer 2

Here's the formula

Answer 3

Okay? Yes I got that part...

Answer 4

I have to convert both of the distances to radians right?

Answer 5

The formula states arc length = radius * central angle
So the formula converts to
central angle = arc length / radius
and yes convert to radians

Answer 6

or shouldn't only ONE of them be converted into radians because like, if it's measured in radians, and we're dividing the 2, then we would cancel out...like..one of the radians in the division.

Answer 7

so ARC LENGTH needs to be converted into radians

Answer 8

wait but then there will still be a unit of measurement in the bottom...

Answer 9

OH OH

Angle is arc length/radius

Arc length is cm
Radius IS a radian. Radius = radian

Answer 10

So basically

cm * (rad/cm) = rad

Answer 11

and in my example, 12.2cm * (1rad/133.4cm) = answer

Answer 12

No arc length is a distance measurement in this case
so angle in radians = 12.2/133.4

Answer 13

Same thing as cm * (rad/cm)

You just cancelled out the cm ahead of time.

Answer 14

Yes, I like to simplify wherever I can.
So your answer is (12.2/133.4) radians

Answer 15

K ty.

Answer 16

glad to help :-)