Formulas & tables/Physics/Dynamics/Torque

Torque

M=Frsin⁡αM=F r\sin\alpha

Result unit: N·m

What it describes

A measure of the rotational effect of a force; it depends on the force, the lever arm and the angle between them.

Symbols

MM
torque
[N·m]
FF
force
[N]
rr
lever arm
[m]
α\alpha
angle between the force and the lever arm
[°]

Where it comes from

How effectively something turns depends not only on the force, but also on the lever arm (the distance from the axis) and the angle — it is best to push perpendicularly (sin⁡90∘=1\sin 90^\circ=1) and as far from the axis as possible.

When to use it

Levers, pulleys, equilibrium of rigid bodies. Condition for rotational equilibrium: the sum of the torques = 0.

Example

A force of 10 N acts perpendicularly on a lever arm of 0.4 m. Find the torque.
SubstitutionF=10F=10 N, r=0.4r=0.4 m, α=90∘\alpha=90^\circ.
ResultM=10⋅0.4⋅1=4M=10\cdot0.4\cdot1=4 N·m.

Related formulas

Newton's second law Angular momentum

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