# if a force is 1 newton metre, what is it at 2 meters?

If I have a force, say 24 kg/cm what would that equate to at 2cm? I would like to know the formulae for calculating this. For example. If a motor can hold an object of 24kg at 1cm from its pivot point, what is it cable of holding at 5cm? And how is it calculated?

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Oops, spelled metre wrong. I accidentally spelt it the American way – Mark W May 29 '11 at 15:15
This looks suspiciously like a homework problem. Have you tried the wikipedia article on forces, tension or Newtonian mechanics? – C Earnest May 29 '11 at 15:40
Nope. I am calculating lifting capabilities for a robot ARM for hobby robotics. I have googled for ages and cannot find the answer – Mark W May 29 '11 at 15:47
This sounds like what you are talking about: en.wikipedia.org/wiki/Torque If it is not, could you maybe provide more details about the robot arm? – C Earnest May 29 '11 at 16:05
I have no details yet. I am playing with ideas to see what motor, arm length will be able to lift what, within my budget. – Mark W May 29 '11 at 16:30

The units you mean are probably kg*cm (sometimes written kg.cm in robotics). Your original specification of 24 kgcm is a torque and not a force. The difference in practice is that, as the units imply, your resulting force at a point a distance from the "pivot point" decreases by the distance. So 24 kg*cm means that it can hold 24 kg at 1 cm or 12 kg at 2 cm etc.

Notice that strictly speaking kg is not a standard unit of force in physics since the force of gravity on a kilogram varies. In robotics, this seems to be the standard unit of servo torque though.

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That's not what those units mean! 10 kg/cm would mean 10 kg at one cm, 20 kg at 2 cm, etc. (Compare with 60 miles/hour: 60 miles in 1 hour, 120 miles in 2 hours, etc.). But anyway, kg/cm don't seem to be the correct units here -- certainly, those aren't anything like the units of a force! I think C Earnest is right that what's being talked about here is really a torque, although it's hard to tell for sure. Torque comes in units of force times distance, not force per distance (N m vs. N/m). If what's being specified is a torque, then it does scale as you said: 2x the distance, 1/2 the force. – Ted Bunn May 29 '11 at 19:28
@Ted: ah sorry, both the OP and me must have misread; in robotics, the torque is specified in kgcm and not kg/cm :) I'll just remove the / sign from the post.. i've seen that servo spec so many times I just didn't notice the extra slash.. – BjornW May 29 '11 at 19:46
I was indeed refering to a torque. And have researched some more and discovered the lifting capability at 3cm would equal 8kg. (24/3=8) I believed the problem to be more complicated than it was. The only complicated part for me is factoring the weight of the lever itself. Thanks for all the help guys. – Mark W Jun 1 '11 at 12:30