Rolling disks + relative rotation on a large disk
Knowledge bridge
Step 1: relate arc lengths so the small disks roll without slipping on the large circumference (geometry of contact). Step 2: convert path radius R+r into orbital and spin rates (ω/51-type ratios). Step 3: close the remaining angular gap 2π − Δθ to get the meeting time τ.
Why it feels hard
Easy to use the wrong Δθ (2/51 vs 4/51) if relative rolling sense is mishandled.
What to practise
Always draw contact velocities and write v = ωr for every rolling interface before algebra.