What is the relationship between angular velocity and linear speed?
v = rω tangential velocity = radius x angular velocity PROOF: The tangential velocity, or linear speed of the particle, is the rate at which it moves around the circumference or arc of the circle. On the other hand, the angular velocity is the rate at which the particle sweeps through an angle θ. Since velocity is distance / time, the formula for tangential velocity is: v = ∆l/∆t where l = arc length, t = time using the relation l = rθ (arc length = radius × angle swept out): v = ∆l/∆t = r ∆θ/∆t However, we (hopefully) recall that angular velocity ω is defined as the angle swept out per unit time, or ω = ∆θ/∆t .: v = r ∆θ/∆t = rω ————————————–… To finish off, it may help to memorise these three relationships between linear and rotational motion.
