How do you tell which way a gear turns?

Every time two gears mesh, the direction reverses. Number the gears in a line starting from the driver: odd-numbered gears turn the same way as the driver, and even-numbered gears turn the opposite way.

How do you work out the speed of a driven gear?

Multiply the driver's speed by the driver's tooth count and divide by the driven gear's tooth count. A driven gear with twice the teeth turns at half the speed; one with half the teeth turns at twice the speed.

What does an idler gear do?

An idler sits between the driver and the last gear. It reverses the direction of everything after it, but it does not change the overall speed ratio, because its own tooth count cancels out. Only the first and last gears in a simple train set the speed.

If a gear turns faster, does it have more force?

No, less. In an ideal gear train, torque (twisting force) changes in the opposite direction to speed, by the same ratio. A gear that turns twice as fast delivers half the torque, ignoring friction.

Do belts and chains reverse direction like gears?

No. Wheels joined by a straight belt or chain turn the same way, like a bicycle's pedals and rear wheel. A crossed belt, looped in a figure eight, reverses the driven wheel. The speed rule is the same as for gears: the bigger wheel turns slower.

How Do Gears Work? A Firefighter Mechanical Aptitude Question, Worked Step by Step

To answer a gear question, do two things in order: work out the direction first, then do the arithmetic. A common mistake is doing the arithmetic first and guessing the direction.

Below are the two rules, one original question worked through step by step, and the mistake behind each wrong answer.

Which way does a gear turn?

Every mesh reverses the direction. Where two gears touch, their teeth move the same way at the contact point, so if one turns clockwise, the gear it drives turns counter-clockwise. In a line of gears, number them from the driver: the odd-numbered gears turn the same way as the driver, and the even-numbered gears turn the opposite way.

Work out the direction before any calculation. On a multiple-choice question, direction alone often rules out half the options.

How fast does a driven gear turn?

Teeth pass the contact point at the same rate on both gears, so a gear with more teeth takes longer to go round. The rule is:

driven speed = driver speed × driver teeth ÷ driven teeth

A driven gear with three times the teeth turns at one third of the speed. A driven gear with half the teeth turns twice as fast.

In an ideal gear train, torque, the twisting force a shaft delivers, changes in the opposite direction to speed by the same ratio. Slow it down by 3 and you get 3 times the torque; speed it up by 2 and you get half.

What is an idler gear?

An idler is a gear placed between the driver and the last gear in a line. It changes the direction of everything after it, but it does not change the overall speed ratio. Its teeth appear once as a driven gear and once as a driver, so they cancel out. In a simple line of gears, only the first and last gears set the speed.

Many gear-train questions test this rule. A large idler in the middle of a drawing adds arithmetic you do not need, and treating its size as if it sets the speed gives a wrong answer.

Can you solve this gear question?

Try it before you read the working. The question was written for this post, and its numbers are chosen to keep the arithmetic clean.

Three gears sit in a line. Gear A, the driver, has 20 teeth and turns clockwise at 60 revolutions per minute (rpm). It meshes with gear B, which has 40 teeth. Gear B meshes with gear C, which has 10 teeth. Which way does gear C turn, and how fast?

A. Clockwise at 120 rpm

B. Counter-clockwise at 120 rpm

C. Clockwise at 30 rpm

D. Counter-clockwise at 240 rpm

How do you work out the answer?

The answer is A: clockwise at 120 rpm. Gear C is the third gear, so it turns the same way as the driver, and the idler cancels out of the speed, leaving 60 × 20 ÷ 10 = 120 rpm. Here is each step.

Step 1: Direction. Number the gears: A is 1, B is 2, C is 3. Odd gears turn with the driver, so C turns clockwise like A. This rules out options B and D.

Step 2: Find the gears that set the speed. B sits between A and C, so it is an idler. Only A and C matter for the speed.

Step 3: Apply the rule. Driven speed = 60 × 20 ÷ 10 = 120 rpm.

Step 4: Check it the long way. A drives B: 60 × 20 ÷ 40 = 30 rpm, counter-clockwise. B drives C: 30 × 40 ÷ 10 = 120 rpm, clockwise. Both routes agree, and B's 40 teeth appear once on top and once underneath, which is why they cancel.

Step 5: Check the result. Gear C is smaller than gear A, so it should turn faster, and 120 is faster than 60. In an ideal train it also delivers half of gear A's torque, because it turns twice as fast.

Why are the other answers wrong?

Each wrong answer comes from one specific mistake.

B, counter-clockwise at 120 rpm, has the right speed and forgets that the idler reverses the direction a second time. Two meshes means two reversals, which puts C back where A started.
C, clockwise at 30 rpm, has the right direction and the ratio upside down: 60 × 10 ÷ 20. The smaller gear turns faster. A quick check catches this: a smaller driven gear can never turn slower than its driver.
D, counter-clockwise at 240 rpm, uses the idler's teeth as if B were the driver turning at A's speed: 60 × 40 ÷ 10. It also gets the direction wrong. The idler's size does not affect the speed of gear C.

What changes if a belt replaces a gear?

Direction changes, and speed does not. Wheels joined by a straight belt or chain turn the same way, because nothing meshes to reverse them. A crossed belt, looped in a figure eight, does reverse the driven wheel. The speed rule is the same idea as for gears: the bigger wheel turns slower, in proportion to its size.

So in a mixed drawing, count only the meshes and the crossed belts as reversals, and ignore the straight belts when you count.

Do firefighter aptitude tests ask about gears?

Many Canadian tests have a mechanical section, but few publish their question topics. Edmonton Fire Rescue Services, for example, lists "maps, diagrams and mechanical reasoning" among the skills its aptitude test assesses, and the National Testing Network describes most FireTEAM mechanical questions as being about basic mechanical objects and principles. Neither names gears.

So treat gear practice as general practice in mechanical reasoning. It is not a preview of any particular test. The habit it builds, working out what must be true before calculating, applies to other mechanical questions as well.

How should you handle gear questions under time pressure?

Use the same order every time:

Direction first. Count the meshes, or number the gears and use odd and even.
Find the first and last gears. Anything in between is an idler for the speed.
Apply the rule once: driver speed × driver teeth ÷ driven teeth.
Check the answer makes sense. A smaller driven gear turns faster with less torque. A bigger one turns slower with more torque.

Where can you practise more gear questions?

Semparo's mechanical practice bank has 500 original questions covering gears, levers, pulleys, hydraulics, tools and valves, each with a worked explanation, and a free account includes 10 of them as samples.

Once you answer single questions reliably, practise with a time limit. The full FireTEAM-style mock runs mechanical alongside human relations, reading and math in timed sections, and you can compare the plans that include the full bank before choosing.

The question in this post is original and was written to teach the direction and ratio rules; it is not taken from any test or prep product. The descriptions of the Edmonton and FireTEAM tests come from Edmonton Fire Rescue Services' recruitment page and the National Testing Network's published material, checked in September 2026. Test content can change, so confirm the current format with your department's posting and the test administrator.