Small hobby motors spin fast, thousands of turns a minute, but with little twisting force. Wheels and arms need the opposite: slow and strong. Gears make the trade.
Key idea
When a gear with $N_1$ teeth drives a gear with $N_2$ teeth, the gear ratio is $N_2 : N_1$. The output turns $N_1/N_2$ as fast, and (ignoring friction) with $N_2/N_1$ times the torque.
Why it works
Each tooth that passes the meeting point is one tooth on both gears. So the big gear must turn less to pass the same number of teeth. Power, speed times torque, stays about the same, so slower means stronger.
Worked example: Slow it down
A 10-tooth gear on a motor at 3,000 rpm drives a 50-tooth gear. How fast does the big gear turn?
- Ratio $50:10 = 5:1$.
- $3000 / 5 = 600\ \text{rpm}$, with about 5 times the torque.
Answer: 600 rpm.
Worked example: Two stages
Two 5:1 stages in a row. What is the total ratio?
- Ratios multiply: $5 \times 5 = 25$.
Answer: 25:1.
Common mistake
Dividing the wrong way and making the slow gear faster. The gear with more teeth always turns slower.
Safety. Gears are pinch points. Keep fingers, hair and loose sleeves away while they turn, and switch off before you reach in.