Year 12s: what will be the first way you research your future options? >>

How do you convert radians into metres, given radius?

I saw an answer on Google that says you use this formula: (x/2pi) r^2 and x is the radian. Don't know if there's any credibility in that though. Is it right?

Reply 1

VannR

Radians are a measure of angle; metres are a measure of distance. You might as well ask how to convert units of mass into units of electrical current.

Reply 2

maggiehodgson

Original post by Airess3

I saw an answer on Google that says you use this formula: (x/2pi) r^2 and x is the radian. Don't know if there's any credibility in that though. Is it right?

Given an angle in degrees, you would find the length of the arc by

(degrees/360) x (formula for circumference)

In radians, as 360 degrees is 2pi, the arc length would be

(radians/2pi) x (formula for circumference)

What do you think now? Was your Google search right?

Reply 3

SnoochToTheBooch

360 degrees is the same as 2*pi = 6.28... radians. If you know the radius then you know the full 360 degree circumference, so you know how far a fraction of that circumference is too.

Reply 4

sanguisuga

Original post by Airess3

I saw an answer on Google that says you use this formula: (x/2pi) r^2 and x is the radian. Don't know if there's any credibility in that though. Is it right?

To find the arc length, you literally just multiply the angle (in radians, not degrees) by the radius!

This is because:

circumference = 2(pi)r
360 degrees (a full circle) = 2(pi) radians

therefore the fraction of the circumference you are measuring is (angle of arc) divided by (angle of full circle)

so you times circumference by that fraction

2(pi)r x (angle)/2(pi)

the 2(pi) cancels out

r x (angle)

hope that makes sense and/or helps! :smile:

Reply 5

vijayshankar

take this l=r*theta, where l gives the linear distance in meters and r is the radius in meters. ( this is a well known formula) . Now equate LHS and RHS meter and meter cancel out and theta becomes dimensionless. That is the idea of radian, unit of angle which is dimensionless.