Torque & the Lever Law

The Lever Law

A force's ability to turn something around a pivot depends on both how hard you push and how far from the pivot you push. The same force applied farther from the pivot creates more turning power, which is why a long wrench loosens a stubborn bolt more easily than a short one.

τ = r · F

• τ — torque (N·m): the turning power of a force around a pivot
• r — lever arm (m): the distance from the pivot to where the force is applied
• F — force (N): the push or pull applied perpendicular to the lever arm

You push perpendicular to a wrench at a point 0.5 meters from the bolt, with a force of 20 N. How much torque do you apply?

• r = 0.5 m
• F = 20 N

1. τ = r · F
2. τ = 0.5 m × 20 N

τ = 10 N·m

The same 20 N force is now applied at a lever arm of 1 meter instead of 0.5 meters. What is the new torque?

• 10 N·m
• 20 N·m
• 40 N·m

A 40 N weight sits 1 meter from the pivot on one side of a see-saw. How much force is needed 2 meters from the pivot on the other side to balance it?

• 20 N
• 40 N
• 80 N