# An intuitive approach to torque's dependence on radius

1. Sep 10, 2013

Does anyone have an intuitive explanation for why torque depends on the perpendicular distance from the axis of rotation? I understand the maths and fully accept the truth of the description, but CANNOT wrap my brain around the reason. The ball and spring model of a solid seems like a place to start? The uneven acceleration of a body's particles must play a role, since this is what defines rotational motion. References to conservation of energy seem to simply beg the question. In terms of the various linear tendencies of component particles, how does an increase in radius actually change the distribution of force on a body?

2. Sep 10, 2013

### SteamKing

Staff Emeritus
It's a definition, T = F * d

No balls or springs required, whatever they are for.

3. Sep 11, 2013

### A.T.

I have two ideas for you:

1) It should be intuitively obvious that a force applied at the center, will not rotate the object (Which way would it rotate, if it did?). So if we accept that an off-center force does rotate the object, there must be some dependency between "the ability to rotate" and "point of application".

2) To understand why "the ability to rotate" is proportional to the lever arm, it is useful to consider a static case, where a small force counters a greater force rotationally. The proportionality can be derived from static linear forces only, without invoking conservation laws. See the PDF posted by Phillip Wood in post #10 here: