Gears
Turn one gear and the whole machine moves. Engineers, soldiers and technicians are tested on seeing how. Can you?
The blue gear turns as its arrow shows.
Which way does each lettered gear turn, and which one turns fastest?
Four rules are all it takes. Read on, then try the test.
Where it appears
Gear and belt questions are a staple of mechanical reasoning (or mechanical comprehension) tests, which measure how well you understand how simple machines move. You will meet them in:
Those tests usually ask about a single picture with no time pressure. Here the trains grow longer and the rules combine as you get better, so it trains the habit those questions reward: trace the motion link by link instead of guessing from the picture.
The questions, and the four rules that answer them
The blue gear drives the train. Four gears carry a letter, and the question asks for one of them:
- Which gear turns clockwise (or anticlockwise)?
- Which gear turns fastest?
- Of the gears turning clockwise, which is fastest?
1Gears that touch: opposite ways
Two gears whose teeth mesh turn in opposite directions. Along a chain of touching gears the direction flips at every contact, so count the contacts from the blue gear: an even number means the same way as the blue gear, an odd number the other way.
The size of the gears makes no difference to the direction.
2An open belt: the same way
A belt that runs straight round two wheels (two runs side by side) turns them in the same direction. The belt runs on a darker pulley fixed to each gear's face.
3A crossed belt: opposite ways
A belt whose runs cross in an X between the wheels turns them in opposite directions, just like two touching gears.
4Two gears on one axle: together
A small dark gear fixed on top of a big one shares its axle: the two are one piece and turn the same way, at the same speed. A gear drawn lying over the big gear meshes with the small one on top.
Speed: which gear turns fastest
Where two gears touch, their teeth pass each other one by one, so their rims move at the same pace: the rim speed, in teeth per turn of the blue gear. A gear's turning speed is its rim speed divided by its number of teeth:
speed = rim speed ÷ teethA belt carries the rim speed the same way from pulley to pulley. So along touching gears and belts the rim speed never changes, and a smaller gear turns faster: a 13-tooth gear driven by a 26-tooth one turns twice as fast.
Gears in between change nothing
Here a 26-tooth blue gear drives a 12-tooth gear, which drives another 26-tooth gear. The small gear in the middle spins fast (26 ÷ 12 = 2.17), but the gear at the end turns at 1.00, exactly as fast as the blue gear: same rim speed, same size. Only the first and last sizes matter along a plain train.
An axle pair changes the rim speed
Two gears on one axle turn at the same speed, but their rims do not move at the same pace: the big gear's rim is longer. When the blue gear (20 teeth) drives the small gear of a pair (12), the pair turns at 20 ÷ 12 = 1.67, and the big gear (26) hands on a rim speed of 1.67 × 26 = 43 teeth per turn instead of 20. The 12-tooth gear it drives turns at 43 ÷ 12 = 3.61.
Direction and speed together
The hardest questions ask "Of the gears turning clockwise, which is fastest?". Work in two passes: first find which lettered gears turn the asked way (rules 1–4), then compare only those for speed. The fastest gear of all four always turns the other way, so ranking by speed alone picks the wrong one.
Two questions, solved
1A direction question
Which gear turns anticlockwise?
Try it first, then open the answer.
Show the answer: gear A
- The blue gear turns anticlockwise.
- It touches gear D, which turns the other way: clockwise.
- It touches the next gear, which turns the other way: anticlockwise.
- A crossed belt takes it to the next gear: the other way, clockwise.
- It touches the next gear, which turns the other way: anticlockwise.
- An open belt takes it to gear A: the same way, anticlockwise.
2A speed question
Which gear turns fastest?
Try it first, then open the answer.
Show the answer: gear A
- Count speeds in turns of the blue gear: its rim moves 26 teeth for each of its turns.
- It touches the next gear (12 teeth): the rim speed carries over, so it turns 26 / 12 = 2.17.
- It shares an axle with a 26-tooth gear, which turns at the same speed (2.17); its rim moves 56 teeth per turn of the blue gear instead of 26.
- It touches gear A (16 teeth): the rim speed carries over, so it turns 56 / 16 = 3.52.
Every lettered gear's speed:
How the practice test runs
- 3:00 on the clock, and it only runs while a question is on screen.
- Levels: a chain of gears first, then branches, belts, crossed belts, axle pairs, speed questions, and at the top direction and speed together.
- The ladder: until your first miss, every right answer jumps a whole level; after it, three right answers in a row jump a level and a miss drops one. Your level carries over to your next session.
- Scoring: a right answer earns the question's points (harder questions pay more), a wrong one costs half as many, so guessing does not pay.
- Every question is new, and the review after a session draws every gear's turn and speed.
Try the Gears test
Free and adaptive, no account needed. Start with a short chain and climb to belts, axle pairs and speed questions.
Start the Gears test Also in the IQ Test & Brain Training app