What is torque?

A force can push something along, but it can also make it turn. The turning effect of a force is called torque (also the moment of a force). It depends on two things: how hard you push, and how far from the pivot you push. τ = F × r.

Torque is measured in newton-metres (N·m). Push with 100 N on a spanner 0.5 m from the nut and you apply 50 N·m. Push with the same 100 N only 0.1 m from the nut and you get just 10 N·m. That is why spanners have long handles and door handles sit far from the hinges.

Only the part of the push at right angles to the spanner turns it. Push at an angle θ and τ = F r sin θ. Push straight along the handle, towards or away from the nut, and there is no torque at all. Another way to see it: torque is the force times the lever arm, the shortest distance from the pivot to the line the force acts along.

A stuck nut is held by friction in its threads. It won’t move until your torque beats its breakaway torque. Then it turns. Torque is to turning what force is to moving, so it sits right next to Newton’s laws (see NewtonClear and ForceClear).

When two torques twist in opposite directions, they can cancel. Then nothing turns: the object is balanced. This is the principle of moments: for balance, the clockwise moments equal the anticlockwise moments.

On a seesaw, each child’s weight pulls down at their seat. A heavy child near the middle can balance a light child far out: m₁ × d₁ = m₂ × d₂. A 40 kg child 1.5 m from the pivot balances a 30 kg child 2 m out. Archimedes wrote this down about 2,250 years ago. The metre rule balance in your school lab is the same thing with grams and centimetres.

Gravity pulls on every bit of an object, but it acts as if all the weight sits at one point, the centre of gravity (CG). An object stands as long as the line straight down from its CG falls inside its base. Tip it past that and its own weight makes a torque that turns it over. Heavy things on a cupboard’s top shelf raise its CG, so it topples at a smaller tilt. Double-decker buses are tilted to 28° in a test to prove they won’t roll over.

A tightrope walker is balancing on a line, so any lean grows. A long pole spreads mass far from the rope, which raises the moment of inertia: the same gravity torque turns the walker more slowly, and that buys time to correct (see InertiaClear).

Most machines deliver their work by turning, so their strength is a torque. On a bicycle your foot pushes on a crank 17 cm long. Push down with 400 N when the crank is level and you apply 400 × 0.17 = 68 N·m. At the top and bottom the crank points along your push, so the torque drops to zero: that’s why your legs take turns.

The chain carries that torque to the back wheel. The gears change it: a rear cog with more teeth than the chainring turns the wheel with more torque but fewer turns. That is why a low gear helps you climb (see CycleClear). The wheel’s torque divided by its radius is the push of the tyre on the road.

Engines are tested on a brake: a band grips a drum on the shaft and a lever arm presses on a scale. Torque = scale force × arm length. A typical 1.2 litre car engine makes about 113 N·m, a 150 cc motorcycle about 13 N·m, a mixer grinder’s motor under 1 N·m and a ceiling fan’s about 1 N·m.

So why is the mixer so powerful? Power = torque × spin speed, P = τ ω, with ω in radians per second. The mixer spins at over 12,000 rpm, so a small torque still gives hundreds of watts. The car engine’s power peaks at about 66 kW near 6,000 rpm, even though its torque peaks lower down (see CarClear, MotorcycleClear, MixerClear and FanClear).

Once you know τ = F × r, you see it everywhere. When a job needs a certain torque, a bigger radius means a smaller force.

A steering wheel is big so your hands work far from the column. Old lorries and buses without power steering had huge wheels for exactly this reason. A screwdriver with a fat handle lets your grip act further from the screw’s axis, so the same grip gives more torque.

A nutcracker is a lever with its hinge at one end. Squeeze far from the hinge and the nut, close to it, feels many times your squeeze: F_nut × a = F_hand × b. A wheel brace works the same way. Slide a pipe over its handle and your push acts twice as far out, so it makes twice the torque. Your force doesn’t grow, the torque does. A torque wrench goes the other way: it clicks when you reach the right torque, so a nut is tight but not over-tight. Never extend a torque wrench with a pipe.

Your forearm is a lever too, but a backwards one. The biceps pulls only about 4.5 cm from the elbow, while a load sits about 35 cm out in your hand. So the muscle must pull about 8 to 9 times the load. You trade force for speed and reach (see SkeletonClear).

A torque that isn’t balanced doesn’t just hold things: it makes them spin faster. τ = I α is Newton’s second law for turning (see NewtonClear). Here α is the angular acceleration, and I, the moment of inertia, is how hard the thing is to spin. Mass far from the axis counts much more than mass near it (see InertiaClear).

A spinning gyroscope is the big surprise. Rest one end on a post and gravity’s torque should tip it over. Instead it swings slowly round the post. The torque changes the direction of its spin rather than tipping it. This is precession. Spin it slower and it precesses faster, until the spin is too slow and it falls.

Myth: “torque and work are the same, because both are N·m.” No. Torque is a turning force; work is energy. A torque only does work when it turns something: W = τ × angle (in radians), in joules. Lean 100 N·m on a stuck nut and you do no work at all. That’s why torque is always written N·m and never J.

Myth: “a longer spanner gives more force.” Your push stays the same. What grows is the lever arm, and so the torque.

Myth: “more torque means faster.” First gear gives the wheels about five times the torque of fifth gear, yet the car is slow in first. Gears trade torque for turning speed. Top speed comes from power, P = τ ω, and the power is the same in every gear.