Aptitude skill lesson
Mechanical comprehension: skill lesson
Mechanical comprehension is the ability to predict what a physical system will do (which way a gear turns, how hard you have to pull, how far the load actually rises) from forces, moments and the simple machines, rather than from a memorised formula sheet. It carries real weight in apprenticeship entry batteries, military technical selection, and screening for maintenance, machine operation and rigging roles. The same reasoning is daily work on site: sizing a jack, choosing a block-and-tackle arrangement, deciding why a belt slips under load but not at idle. Practice here is device-local: no account, and nothing leaves this device unless you export it.
Published · last reviewed
Applies to Novus Learn 0.1.0
What changed, and when
- , Replaced the body of all 27 non-judgement lessons with construct-specific material: six worked examples each, carrying the actual arithmetic, the actual inference or the actual procedure, plus expanded objectives, practice tips and glossary. Every 'Related Learn topics' link now points at a real page on this site rather than a generic search. The eight workplace-judgement lessons are unchanged.
- , Rebuilt the lesson page around a sticky contents rail, per-section links, previous/next lesson navigation, and two graded checkpoints drawn from the open practice bank.
- , Repaired the aptitude integrations behind the lessons so each one links to skill-specific practice instead of the unscoped fixture engine.
- , Published one lesson for each of the 35 aptitude skill constructs: objectives, worked examples, practice tips, glossary, Learn topic links, and sources.
These 35 skill lessons are authored and revised as one set, so they share one revision history rather than 35 identical dates.
Objectives
Copy link- Balance moments about a pivot (effort x effort arm = load x load arm) and name whether a given tool is a first-, second- or third-class lever.
- Work out the speed, torque and rotation direction of a driven gear from tooth counts, including what an idler gear does and does not change.
- Count the rope parts that support a moving block to get the mechanical advantage of a pulley system, then state how much rope must be pulled per metre of lift.
- Apply pressure = force / area to a hydraulic jack and predict the piston-travel penalty that comes with the force gain.
- Predict rpm across a belt or chain drive from pulley or sprocket diameters, and say when slip breaks the prediction.
- State the trade-off that governs every simple machine: multiplied force always costs distance, and friction always makes the delivered advantage smaller than the ideal one.
Checkpoint: does the idea land?
Copy linkBefore the worked examples, check that the objectives above actually landed.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Examples
Copy linkLevers: balance the moments, then name the class
A wheelbarrow carries 60 kg whose centre of mass sits 0.4 m from the wheel axle, and you grip the handles 1.2 m from that same axle. Take moments about the axle: lift force x 1.2 m = 60 kgf x 0.4 m, so the lift force is 60 x 0.4 / 1.2 = 20 kgf, about 196 N. The mechanical advantage is simply the arm ratio, 1.2 / 0.4 = 3. Two traps live in this item. The first is measuring the load arm from your hands instead of from the fulcrum; the arm is always the perpendicular distance to the pivot, and the pivot here is the wheel contact, not the barrow body. The second is calling it a first-class lever because that is the one everyone pictures. A wheelbarrow is second class: fulcrum at one end, load in the middle, effort at the far end, which is why its mechanical advantage is always greater than one. Compare tweezers or a pair of tongs, where the effort sits between fulcrum and load: that is third class, mechanical advantage below one, and you are deliberately trading force away to buy speed and control at the tip. Your own forearm lifting a weight is the same arrangement, which is why a 5 kg dumbbell loads the biceps far more than 5 kg.
Gear trains: tooth counts set speed, meshes set direction
A 12-tooth driver turning at 300 rpm meshes directly with a 36-tooth gear. The ratio is driven teeth over driver teeth, 36/12 = 3:1, so the output turns at 300/3 = 100 rpm and, ignoring friction, carries about three times the torque. One external mesh reverses rotation, so the output turns opposite to the driver. Now drop a 20-tooth idler between them. Step it through: 300 x 12/20 = 180 rpm at the idler, then 180 x 20/36 = 100 rpm at the output. The overall ratio is unchanged at 3:1, the idler's tooth count cancels, but there are now two external meshes, two reversals, so the output turns the SAME way as the driver. That is the whole reason idlers are fitted. The tempting wrong answer treats the idler as another reduction stage and reports 180 rpm or some product of both ratios. The check that never fails: only the first and last gear in a simple train affect the ratio, and the direction depends on whether the number of external meshes is odd (reversed) or even (same). An internal or ring mesh, as in a planetary set, does not reverse at all.
Pulleys: count the rope parts that carry the load
A 200 kg load, about 1,962 N. Hung from a single pulley bolted to a beam, the pulley only changes the direction you pull; both rope parts still meet at a fixed axle, the mechanical advantage is 1, and you pull the full 200 kgf. Hang the pulley on the load instead, with one rope end anchored above and the other in your hands, and two rope parts now support the moving block: mechanical advantage 2, effort about 100 kgf or 981 N, but you must pull 2 m of rope for every 1 m the load rises. Build a tackle with four parts supporting the moving block and the effort falls to 200/4 = 50 kgf, about 490 N, at the cost of 4 m of rope pulled per metre of lift. The trap is counting sheaves instead of supporting parts. A three-sheave arrangement gives three parts if the dead end is made off to the fixed block and four if it is made off to the moving block, and the answer differs by 33 percent. The second trap is treating the figure as delivered force: real sheaves lose a few percent each to bearing and rope friction, so quoted mechanical advantage is the ideal velocity ratio, and the effort you actually feel is higher.
Hydraulics: pressure is shared, force and travel are traded
A jack has a 2 square centimetre input piston and a 50 square centimetre output ram. Push the small piston with 100 N and the pressure in the fluid is 100 / 2 = 50 N per square centimetre, which is 500 kPa. Pascal's principle says every part of the confined fluid sees that same 500 kPa, so the large ram feels 50 N/cm2 x 50 cm2 = 2,500 N. Mechanical advantage 25. Nothing is free: fluid is effectively incompressible, so volume in equals volume out. A 25 cm stroke on the small piston moves 2 x 25 = 50 cubic centimetres, and 50 cubic centimetres spread over a 50 square centimetre ram raises it 1 cm. Twenty-five centimetres of pumping buys one centimetre of lift: exactly the force-times-distance bargain a lever strikes. Candidates lose this item by assuming both pistons travel the same distance, or by concluding the jack manufactures energy. A related item asks about a tank: the pressure at the bottom depends on the height of fluid above and its density, not on the width of the vessel, so a narrow 3 m standpipe reads the same bottom pressure as a 3 m deep swimming pool.
Belts and chains: same belt speed, different rpm
A motor pulley 100 mm in diameter runs at 1,450 rpm and drives a 250 mm pulley through an open V-belt. The quantity that is genuinely shared is belt speed, not rpm, so the driven pulley turns at 1,450 x 100/250 = 580 rpm. Note the direction of the ratio: with gears you divide by driven teeth, with belts you divide by driven diameter, and the arithmetic looks the same only because both are proportional to circumference. An open belt drives both pulleys the same way; a crossed belt reverses the driven pulley, which is the entire point of the classic crossed-belt diagram item. The trap is slip. A flat or V-belt under an overload slips, so the driven speed falls below 580 rpm while the motor holds 1,450: the symptom of a glazed belt or a weak tensioner. A chain or a toothed timing belt physically cannot slip a tooth without damage, which is why camshaft and indexing drives use them and why a belt-driven answer and a chain-driven answer to the same question can legitimately differ.
Springs in series and parallel: the answer most people reverse
Two identical coil springs, each 20 N/mm. Mount them side by side, both carrying the same load, and they act in parallel: stiffness adds to 40 N/mm, so a 400 N load compresses the pair 400/40 = 10 mm. Now stack them end to end, in series. Each spring carries the whole 400 N, force is not split down a chain, so each deflects 400/20 = 20 mm and the total is 40 mm. The combined stiffness is 400/40 = 10 N/mm, half of one spring. Most candidates reverse the two because 'series' sounds like the case where things add. Two reliable checks: in parallel the arrangement is always stiffer than one spring, and in series it is always softer than the softest spring. That is also why suspension designers add a helper spring in parallel to raise rate under load, and why a long slender bolt clamps more forgivingly than a short stubby one carrying the same preload.
Checkpoint: can you apply it?
Copy linkNow apply it. These come from a later section of the bank, so they are not more of the same.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Practice tips
Copy link- Sketch the free body and mark the pivot before writing a single number. Mechanical items are lost by choosing the wrong fulcrum far more often than by mis-multiplying.
- Fix the three lever classes to a tool you can picture (pliers and a see-saw for first class, a wheelbarrow and a nutcracker for second, tweezers and your own forearm for third), and say the class out loud before answering.
- Sanity-check every answer against the work rule: if a machine multiplies force it must divide distance. An answer where the effort both moves less and is smaller than the load is wrong somewhere.
- Convert units before you multiply, not after. A moment computed with millimetres on one side and metres on the other is off by a thousand and looks perfectly plausible.
- For any direction question, walk the mesh or the belt with a finger: each external gear pair reverses, an internal or ring mesh does not, an open belt keeps direction and a crossed belt flips it.
- Work untimed until you can explain the reasoning aloud, then add the clock. Attempts are recorded on this device only, so a messy first pass through gear trains costs you nothing but time.
Glossary
Copy link- Moment (torque)
- A force multiplied by the perpendicular distance from its line of action to the pivot, in newton-metres. A body is in rotational balance when clockwise moments equal anticlockwise moments about the same point.
- Fulcrum
- The pivot a lever turns about. Its position relative to the load and the effort defines the lever class and therefore whether the tool multiplies force or multiplies movement.
- Mechanical advantage
- Output force divided by input force. Ideal mechanical advantage is the geometric figure; actual mechanical advantage is what you get after friction, and it is always lower.
- Velocity ratio
- Distance moved by the effort divided by distance moved by the load. In a lossless machine it equals the ideal mechanical advantage, which is why force gain always costs travel.
- Gear ratio
- Driven teeth divided by driver teeth. A ratio above one reduces speed and multiplies torque; only the first and last gear of a simple train affect it.
- Idler gear
- A gear placed between driver and driven purely to add a mesh. It reverses the output direction and bridges a distance without altering the overall ratio.
- Pascal's principle
- Pressure applied to a confined fluid is transmitted undiminished to every part of it, which is what lets a small piston at high pressure produce a large force on a bigger ram.
- Head
- The height of a fluid column above a point. Pressure at depth is density x gravity x height and is independent of the vessel's width or shape.
Sources
Copy link- Worked examples written for Novus Learn from standard introductory mechanics: moments about a pivot, gear ratios from tooth counts, rope-part counting for tackle, and Pascal's principle.
- Terminology checked against the public Wikipedia articles 'Simple machine', 'Lever', 'Gear train' and 'Pascal's law'. Definitions only; every number and item above is original.
- Novus Learn aptitude construct registry (catalog seed) for the construct scope and related suite mapping.
- Public educational framing only: not affiliated with any official exam board, publisher or employer, and no copyrighted test item is reproduced.
Your notebook for this lesson
Saved sections and notes are kept in this browser, on this device. No account is required, and nothing is sent to us unless you create one and switch on backup. They travel with your backup file from My Learning, and they are lost if you clear this site’s data.
Saved sections
None yet. Use Save beside any section heading above to keep it here.
4000 characters left
Your own words, so you can find this again from any other lesson. Up to 12.