# Applying torque away from centre of mass

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I can apply a force to a point on my rigid body simulator, which generates a force and a torque. I can also apply a torque about the CofM, but how do I apply a torue about a different point. This should apply both a torque and a force I think. It's something to do with doing the normal torque clculation and then another treating the body as a point mass some distance away #I believe?

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Apply a torque? There is no such thing :)

If you want to grab hold of a point and "twist" it then it has the same effect no matter where you are relative to the center of mass (I'll do the maths to show you why if you really care ;) but basically just assume all torques are applied at the CofM.

If you actually want the end result to be that the object rotates around a particular point, then that is a little trickier, but what would you be modelling that requires that?

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I think i see what youre saying. Say you have a pop bottle floating in space and you throw a ball at it and hit it at its very top. The bottle will both rotate(about its CofM) but also translate as well. The torque will be some force applied at a distance from the center of mass, but part of that force will go to translating the object. Id have to break out my dynamics book to do the math, but I believe that objects not pivoted, in free space, will always rotate about their center of mass.

Basically your force that applies to the torque would be a function of the angle of the bottle. At the beginning it should be pure rotation right? Then as you move it less of the force goes into torque because the normal between the two gets smaller(from rotation.) Its like if the bottle was laying on its side in space, and you applied a force only in the +X direction, it would be total translation because the normal between F and (X_cm,Y_cm) is zero. But if you had it standing up and applied it do some point it would be:
Assuming the Force = only in X direction.

normalD = (Y_f - Y_cm)
T(t=0) = F*normalD = F*(Y_f-Y_cm)

Ahh the more I think about it the harder it will get(but not too hard). Remember you need angular momentum and linear momentum now if the object has mass. And you need your moments of inertia for the object. I wonder if using Lagrangian kinetics would be easier. L=T-U right?

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Why not use the correct term for force applied at a point distant to the CoM... moment. Throwing an object at a bottle floating in space applies a force at the contact point. This force MAY be described in other terms due to the moment it creates.

Timkin

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The situation is a car. The rear wheels havce a torque applied, this causes a reactionary torque to try and make the car do a wheelie. How do I approach this - basically applying a torque/moment about the axle?

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i'm remembering,something like that was discussed very much on gamedev.ru.... that was hyper-flamewar[flaming][embarrass][grin].

If you're applying force,no matter to what point,no matter if it causes object to spin or not,center of mass will be accelerated as
A=F/m
.It always was hard to explain to people,that force are not "splitten" into rotating and translating parts that somehow "must in summ give original force".

If you're trowing balls at bottles, both momentum and angular momentum will be same before and after collision..and from that you can find what will happen. When you hit bottle with ball,force depends to point where you hit.

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Quote:
 Original post by DmytryIf you're applying force,no matter to what point,no matter if it causes object to spin or not,center of mass will be accelerated as A=F/m.It always was hard to explain to people,that force are not "splitten" into rotating and translating parts that somehow "must in summ give original force".

I had some problems with this seeming counter-intuitive too :)
There's a good explanation in section 5.5 of the Baraff Unconstrained motion paper.

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In answer to our canine friends question, however, what I said was basically right, I think:

Your car axel applies torque to the car - but think of this instead as applying a set of forces to the car, positioned around the surface of the axel. Some very simple maths shows that any change in position of the axel increases the effect of the force on one side of the axel by exactly the same amount as it decreases the effect of the force on the other (or increases it the same amount in the opposite direction - whatever). Basically, treat your axel as though it was passing through the CofM and your torque will be correct.

But talking about torque is a very rigid-body thing. Start talking about forces and suspension systems and you might notice a few changes... try having a browse through http://ode.org

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But if I could twist the car about an axis where the axle is (obviously need to be very strong), the car would rotate about that axis. If I twist about an axis through the CofM the car twists about that axis. A motorbike generates enough torque at the rear wheel to lift the front wheel of the ground. The further away the wheel axle is from the CofM the harder you have to twist, because of moments and things. Unless the torque is identical, and I also need to act on the moment that is generated?

But basically I want to specify an axis to twist about (can be for special case of one of the body's local axes) and a value for how hard I want to twist. This seems to be to be a torque, but whatever how do I calculate the result from the axis, 'torque', mass and inertial tensor of the car/body?

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