Problem — Torque of a wrench

Problem

A wrench is used to loosen a bolt. A force $F = 80\;\mathrm{N}$ is applied at a distance $d = 30\;\mathrm{cm}$ from the pivot, at an angle $\theta = 60^\circ$ to the wrench. Calculate the torque about the pivot.

Solution

The torque of a force about a pole is $\tau = F\,d\sin\theta$, where $\theta$ is the angle between the force and the lever arm: only the component of the force perpendicular to the arm causes rotation. $\tau = F\,d\sin\theta = 80\cdot 0{,}30\cdot\sin 60^\circ = 80\cdot 0{,}30\cdot 0{,}866$ $\ev{\tau \approx 21\;\mathrm{N\cdot m}}$

Connections

Topics: Dinamica rotazionale Concepts: Momento di una forza Skills: Uso della trigonometria