Q & A: torque and lever arms

Most recent answer: 10/22/2007
Q:
how could you you explain the reqson that a mechanic chooses to undo a tight nut using a long spanner and a door handle is placed well way from its hinges
- ilhan (age 12)
john taylor high school, england
A:
The idea is that of increasing the torque by applying
an external force, like the push of a hand on a door or
the pull of the mechanic's hand on the spanner ("wrench" to readers in the United States), at a farther distance from the axis of rotation.

It's not enough to push or pull far away, but the separation from the axis of rotation to the place where the force is applied needs to be perpendicular to the force (or have a substantial component perpendicular to the force). Pushing on the rim of a merry-go-round along a line pointing at the center pivot will not make it spin. Pushing along the rim will get it spinning. Similarly, pulling on a spanner in a direction perpendicular to the spanner will give the nut a torque proportional to the applied force and to the length of the spanner. This allows a tight nut to be turned with less force (of course the mechanic's hand travels farther if his spanner is longer).

Pushing a door on the side where the hinges are is a good exercise in futility -- the hinges just push back and the door doesn't move. Pushing along a line that goes through the axis of rotation doesn't cause rotation, but pushing on lines that miss the axis of rotation do the job.

(published on 10/22/2007)