If a system with multiple gears aims for equal linear velocity, what must you do regarding gear sizes?

• A. Use a larger gear
• B. Keep sizes the same
• C. Use a smaller gear
• D. Increase the number of gears

Answer: (C)

The main idea is that the linear (tangential) speed at the rim of a gear is v = ωr. When gears mesh, the contact point must have the same tangential speed on both gears, so ω1r1 = ω2r2. If you want every gear in a train to have the same rim speed, you adjust the gear sizes so that this product stays the same as you move along the train. As the angular speed changes through the gear ratios, using a smaller gear for the next stage helps offset the drop in ω and keeps the rim speed constant. A larger gear would push the rim speed higher, keeping the speeds mismatch, and keeping sizes the same or adding gears doesn’t guarantee the same constant rim speed.