The relationship between angular velocity (ω) and linear velocity (v) in circular motion is defined by the equation dθ/dt = v/r, where θ is the angle in radians, v is the linear velocity, and r is the radius of the circular path. The derivation shows that as the arc length (l) is related to the angle by the formula θ = l/r, differentiating this with respect to time leads to the conclusion that rω = v. This confirms that the angular velocity is directly proportional to the linear velocity when considering the radius of the circle.
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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.