Practice question · Multiple choice
Torque is a cross product, and a longer spanner loosens a stubborn bolt more easily. Which feature of the cross product does the spanner exploit?
Hints
- Torque is r × F. Which of the two vectors does the spanner's length change?
- The magnitude is |r||F|sin θ. Ask which factor you are buying.
Show the answer
D. That its magnitude scales with the distance from the pivot
Why
You are buying |r|. The magnitude |r||F|sin θ scales with the lever arm, so a handle twice as long delivers twice the torque from the same push. The sin θ term earns its place too: pushing along the spanner rather than across it gives zero, which is why you push perpendicular without thinking about it.
Practise Cross Product and Geometry in Space
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