Torque: The Cross Product That Turns Things

You'll learnthat torque is the cross product r × F, set by the perpendicular force component.

A wrench pushed at an angle: how much twist? Not the bare r times F. Torque is the vector cross product τ = r × F — its size is set by the part of the force perpendicular to r, and its direction by the right-hand rule, out of or into the page.

8 STEPS · 6 QUICK CHECKS · v2

TORQUE LAB

Before you start

What you're looking at

A wrench on a bolt, pushed r = 2 m from the axis with F = 10 N at θ = 30° to the handle.

The question

How much does that angled push actually twist the bolt?

Watch for

The force splitting into a piece along the handle and a piece perpendicular to it. Only one twists.

What the symbols mean

r = 2 m position vector, F = 10 N, θ = 30°; direction convention: out of the page +k, into it −k.

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