How is dθ/dt related to v/r in circular motion?

[emyt]

Homework Statement

just a conceptual thing I don't quite understand..
how come dtheta/dt = v/r? I thought it was basically the same thing as v = r/t, but with radians..
thanks

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

ω=dθ/dt

now θ is the angle of an arc of a circle of radius r and arc length l.

so θ=l/r

So ω=d/dt(l/r)

r doesn't change so
rω=dl/dt

and dl/dt=v

so rω=v

 

[emyt]

ω=dθ/dt

now θ is the angle of an arc of a circle of radius r and arc length l.

so θ=l/r

So ω=d/dt(l/r)

r doesn't change so
rω=dl/dt

and dl/dt=v

so rω=v

Hi, thanks a lot for the reply. Do we say θ=l/r because the arc length might not be in radians?

thanks

 

[rock.freak667]

Hi, thanks a lot for the reply. Do we say θ=l/r because the arc length might not be in radians?

thanks

Are length is defined as l=rθ when θ is in radians.

 

[emyt]

Are length is defined as l=rθ when θ is in radians.

EDIT: oh never mind, I've got it.. I've somehow forgotten that a radius could be more than 1 unit :P thanks!