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Levers and moments: how do they work?

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University Course Reader · STEM

Taking moments about the pivot, the beam balances when the clockwise and anticlockwise moments are equal.

The reader highlighted one word in a textbook passage. Clicked broke down the physics term “moments” into plain English:

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Overview

A lever is a stiff bar that turns on a fixed point, called the pivot. A moment is the turning effect of a force, and it equals the force times its distance from the pivot. The further from the pivot a push lands, the harder it turns the lever. That is why a small push can lift a heavy load. Apply the push far from the pivot, place the load close to it, and the push makes the larger moment, so the lever turns and raises the load.
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Overview

A lever is a bar turning on a pivot, and a moment is how hard a force turns it: force times distance from the pivot. Physics did not borrow "moment" from "wait a moment"; the two words just crashed, and the physics one is about movement, not time. The working rule is that distance is as good as force. Push twice as far out and you turn the bar exactly as hard as someone pushing twice as hard. Every long handle in your house is that rule, cast in steel. 😎

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Detail

A lever is a stiff bar that turns on a fixed point, called the pivot, and a moment is the turning effect of a force, equal to the force times its distance from the pivot. Slide a crowbar under the edge of a paving slab and let it rest on a brick. The brick is the pivot. Your hands press down on the handle about 60 centimetres from the brick; the slab's edge sits about 5 centimetres from it on the other side. Your push makes a moment that turns the crowbar toward the slab, and the slab's weight makes a moment that resists the turn; whichever moment is larger sets which way the crowbar turns. Your push acts at twelve times the slab's distance, so the crowbar pushes up on the slab's edge with about twelve times your force, and a slab you could never lift by hand moves up. Your end of the crowbar sweeps down through a long arc while the slab edge rises a few millimetres, so the work matches. Your smaller force times its long sweep equals the slab's larger force times its tiny rise. That trade of distance for force is what a lever does, and each end gets one side of it: the end nearer the pivot gets more force, the end further out gets more movement. Engineers call the turning effect a moment, and mechanics call the same quantity torque, measured the same way.
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Detail

A lever is a bar turning on a pivot, and a moment is how hard a force turns the bar: force times distance from the pivot. Try opening a paint tin with a coin. The lid's rim is the pivot, the coin reaches maybe a centimetre past it, and the lid laughs at you. Now slide a screwdriver under the same rim. Same lid, same rim, same push from the same wrist, but the force lands fifteen centimetres out instead of one, so the moment is fifteen times bigger and the lid pops. Nothing about you got stronger between the coin and the screwdriver. The distance did the multiplying, because a moment is force times distance and you just bought fourteen extra centimetres of it. That is why every stubborn thing in your life has a long-handled tool waiting for it. The tool does not add force; it moves your force further from the pivot and lets the multiplication run. One catch to keep you honest: the long handle swings through a big arc to move the lid a millimetre, so you pay in distance what you gained in force. 😎

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Analogy

A wheelbarrow is a lever you have pushed a hundred times. The wheel's axle is the pivot. The load sits in the tray, close to the wheel; your hands hold the handles, far behind it. Your lift on the handles makes a moment about the axle, turning the barrow up; the load's weight makes a moment turning it back down. Your hands sit maybe three times further from the axle than the load, so balancing it takes a third of its weight: you hold sixty kilos of sand up with twenty kilos of lift. Your hands also travel a long arc upward while the tray barely leaves the ground. The smaller lift acts over the longer distance, and the heavier load moves through the shorter one: that is the lever's trade.
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Analogy

A claw hammer pulling a nail is a lever running at full multiplication. The hammer's head sits on the plank as the pivot. The nail is gripped in the claw, a couple of centimetres from that pivot; your hand is at the end of the handle, thirty centimetres out on the other side. Your modest pull, fifteen times further from the pivot than the nail, beats the grip of a nail hammered in to stay, and out it comes. The trade shows while it happens: your hand sweeps through a foot of air while the nail creeps out by a couple of centimetres. A foot of easy pulling buys an inch of nail. That is every lever ever built: distance in, force out. 😎
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Formal definition — The same term, explained the usual way

A lever is a rigid bar free to rotate about a fixed point, the fulcrum (or pivot), used to transmit force between an applied effort and a load. A moment (or moment of force, or torque) is the rotational effect of a force about a point, equal to the magnitude of the force multiplied by the perpendicular distance from the point to the force's line of action (M = F d), measured in newton-metres. The principle of moments states that a body in rotational equilibrium has equal clockwise and anticlockwise moments about any point. Levers are grouped into three classes by the relative positions of fulcrum, load and effort; in each, the ratio of load to effort at balance equals the inverse ratio of their distances from the fulcrum, and the distances moved are in the same inverse ratio, so the work input equals the work output in the ideal, frictionless case.

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