Calculators/Physics/Torque and the lever

Torque and the lever

Torque M = F·r · lever balance

Torque and the lever — illustration

The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force.

Torque M
20 N·m

Torque is a measure of a force's ability to rotate a body about an axis:

M=F⋅rM=F\cdot r

where FF is the force and rr — the lever arm, that is, the perpendicular distance from the axis of rotation to the line of action of the force. The unit is the newton-metre (N·m).

A lever is in balance when the torques on both sides cancel out:

F1⋅r1=F2⋅r2F_1\cdot r_1=F_2\cdot r_2

This is the principle of the lever — a small force on a long arm balances a large force on a short one (hence "give me a place to stand and I will move the Earth").

Examples

F = 50 N, lever arm r = 0.4 m
→ M = 20 N·m
Lever: F₁=30 N, r₁=2 m, r₂=1.5 m
→ F₂ = 30·2/1.5 = 40 N

Frequently asked questions

What is the lever arm of a force?+

The perpendicular distance from the axis of rotation to the line along which the force acts. The longer the arm, the larger the torque for the same force — which is why a longer wrench makes a bolt easier to undo.

How does a lever work?+

It balances torques: a small force on a long arm produces the same torque as a large force on a short one. This way we gain force at the cost of distance.

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