Torque

• 1. Introduction

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  Torque is the twist that turns a screw, spins a wheel, or swings a door, wherever a force acts to rotate something around an axis rather than push it in a straight line. Physicists call it torque; many engineers call the very same quantity moment, or moment of force, depending on which side of a lab bench or a textbook they are standing on. A single screwdriver, turning a single screw, is enough to show the idea in action: the twisting effort applied at the handle is torque. Where did this dual vocabulary come from, and how does the same twisting force decide everything from whether a structure stays standing to how an engine feels at low speed?

• 2. Twist By Another Name

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  The word torque comes from Latin for to twist, and it is credited to the physicist James Thomson, first appearing in print in April 1884. That same year, Silvanus P. Thompson used the term in the first edition of his book Dynamo-Electric Machinery, arguing that a single dedicated word beat borrowing terms like couple or moment, which he felt implied more complicated ideas than a straightforward twist applied to a shaft. In mechanical engineering circles in the UK and the US, though, the older label stuck: moment of force, usually shortened to just moment. That usage can be traced back to at least 1811, in Poisson's treatise on mechanics, a work that did not reach English readers in translation until 1842. Physicists today write torque with the lowercase Greek letter tau, while engineers writing about moment of force typically use the letter M. Whichever name is used, the quantity itself is measured the same way: by how hard something pushes, and how far from the pivot it pushes.

• 3. Measuring The Twist

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  A force of 10 newtons applied at the end of a wrench half a metre long produces a torque of 5 newton-metres, as long as that force pushes perpendicular to the wrench. That relationship, force multiplied by the length of the lever arm, is the simplest way to calculate torque, though it only gives the size of the twist and not its direction. To capture direction as well, physicists treat torque as a vector, found using the right-hand grip rule: curl the fingers of the right hand from the lever arm toward the direction of the force, and the thumb points the way the torque acts. A force aimed straight along the lever arm itself, rather than across it, produces no torque at all. The SI unit for torque is the newton-metre, the same combination of force and distance used across much of physics. That same twisting force does more than hold still. Applied over time, it changes how fast something spins.

• 4. Torque, Motion, And Energy

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  The net torque acting on a body sets the rate at which its angular momentum changes, the rotational version of Newton's second law of motion. Torque even has its own derivative: physicists call the rate of change of torque over time rotatum, a term drawn from the Latin rotatus, meaning to rotate. The word is not universally standardized, but it is commonly used. Torque also connects directly to energy. If a torque acts through an angular displacement, exactly as a linear force does work by acting through a distance, the torque is doing mechanical work, and that work becomes rotational kinetic energy. Divide that work by time and the result is power: the rate at which a spinning object receives energy from an applied torque depends only on how fast it is spinning at that instant, not on whether the spin is speeding up or slowing down. Torque does not have to produce any motion at all, though. Several torques can simply cancel each other out and hold an object perfectly still.

• 5. Balancing The Twists

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  Varignon's theorem, also called the principle of moments, states that the combined torque produced by several forces acting around one point equals the sum of each force's individual torque. That principle underpins static equilibrium: an object stays still only when the sum of all forces acting on it is zero and the sum of all torques acting on it is also zero. In a two-dimensional problem with horizontal and vertical forces, that requirement breaks down into three separate equations, two for the forces and one for the torque, exactly what is needed to solve a statically determinate structure. Torque behaves differently from force in one particular way. When the net force on a system is zero, the torque measured from any point in space comes out the same, regardless of where that point is. A current-carrying loop sitting in a uniform magnetic field is a clean example, since the torque acting on it does not depend on which point is chosen as the reference. Choosing the right reference point matters far less, in other words, than getting the units of the measurement right in the first place.

• 6. Units And Conversions

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  The newton-metre is the official SI unit for torque, and it happens to share its dimensions exactly with the joule, the unit used for energy. The two are not interchangeable, though: torque is assigned to a vector while energy is assigned to a scalar, so the equivalence holds in one direction but not the other, a distinction addressed by a field called orientational analysis, which treats the radian as a base unit rather than as a dimensionless one. Imperial measurements use the pound-foot, or the pound-inch for smaller values, though in everyday American usage torque is more commonly written as foot-pound or inch-pound, with the hyphen in the abbreviation, ft-lb or in-lb, doing the work of signaling torque rather than energy or moment of mass. Converting between power, torque, and rotational speed brings its own constant: American automotive engineers commonly combine horsepower, foot-pounds, and revolutions per minute using a figure of 33,000 foot-pounds per minute for every horsepower, a constant that shifts to roughly 32,550 when metric horsepower is used instead.

• 7. Torque In Engines And Bicycles

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  An engine's power rating is really just its torque multiplied by how fast its drive shaft is spinning, which is why torque forms a basic part of any engine's specification. An internal combustion engine only produces useful torque across a limited range of rotational speeds, typically somewhere between 1,000 and 6,000 rpm in a small car, a curve engineers measure directly with a dynamometer. Steam engines and electric motors behave in the opposite way, producing their maximum torque close to zero rpm and losing torque as speed rises because of friction and other constraints, which is why they can start heavy loads from a dead stop without needing a clutch. A bicycle makes the same relationship easy to feel. A cyclist turns the pedals, cranking the front sprocket, known as the chainring, and the power delivered equals the torque at the crankset multiplied by how fast the pedals are turning. That power then passes through the chain and gears to the road wheels. Switching to a lower gear increases the torque reaching the wheel while reducing its angular speed, and since the two multiply together to give power, the power itself does not change. Torque can be multiplied in only a few ways: lengthening the lever, moving the fulcrum to lengthen one side of it, or running the drive through a speed-reducing gearbox. That same trade of speed for twisting force is the whole job of a gearbox, whether it sits inside a car's transmission or turns a single crank into whatever ratio a rider needs on the next hill.