The discussion revolves around the relationship between angular velocity (dθ/dt) and linear velocity (v) in the context of circular motion, specifically questioning how dθ/dt relates to the formula v/r.
Some participants have provided insights into the relationships between angular and linear quantities, while others are clarifying their understanding of the definitions involved. There appears to be a productive exchange of ideas, with some participants expressing newfound clarity on the concepts discussed.
Participants are navigating assumptions about the units of measurement for arc length and the implications of radius values in their calculations.
rock.freak667 said: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 said: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 said:Are length is defined as l=rθ when θ is in radians.