Two particles A and B are moving in a horizontal plane anticlockwise on two different concentric circles with different constant angular velocities 2ω and ω respectively. Find the relative velocity (in m/s) of B w.r.t. A after time t = π/ω. They both start at the position as shown in figure. (Take ω = 3 rad/sec, r = 2m)

Question

G1 Physics · Accepted Answer

At t=π/ω, A (radius r, angular speed 2ω) completes one full revolution and returns to its initial point, while B (radius 2r, angular speed ω) reaches the diametrically opposite point. Their tangential velocities are opposite, each of magnitude 2ωr. Hence relative speed=4ωr=4×3×2=24 m/s.