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I don't know what the problem is called formally (that's why I didn't find it by searching) and I am happy to be informed of another thread which is answered.

When a force is exerted on an object not tangential to its centre of mass, the force will result in linear motion and rotational motion (assuming we speak of an object not moving before..)

Now I wonder how to calculate the amount of torque and linear force.

example

Example: An impulse of 5N is excerted at 310° (Clockwise) to a circle of radius 1m.

DasEtwas
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1 Answers1

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When you apply a force that is not in line with the center of mass of the object:

  1. the center of mass will accelerate as though the force is applied there
  2. the object will experience a torque $\vec{\Gamma} = \vec{r}\times \vec{F}$, where $\vec{r}$ is the vector from the center of mass to the point where the force acts.

This second point can be put another way - the torque is the product of the force and the "distance of closest approach" of the line of action of the force and the center of mass:

enter image description here

Floris
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  • so you mean the vector r is pretty much a representation of this <---d---> in the picture? – DasEtwas Mar 19 '17 at 20:42
  • Actually no - the vector $\vec{r}$ points to the tip of the force vector. But the cross product for both would be the same - because it takes into account the $\sin$ of the angle between them... – Floris Mar 19 '17 at 20:43
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    The r vector points to the tip of the force vector, but the force vector can be moved freely along it's line of action, so the r vector can point to any position along the force's line of action. – Sam Spade Mar 19 '17 at 21:22
  • $\Gamma$ is a vector so it should be noted as $\vec{\Gamma}$ – John Alexiou Mar 20 '17 at 02:22
  • @DasEtwas an applied force has a line of action which can be fully described by a direction $\vec{e} = \vec{F} / | \vec{F} |$ and the minimal distance $d$ to point of interest (center of mass here). These two describe the geometry of the problem and you can solve this problem qualitatevily at this point. The magnitude $| \vec{F} |$ is needed to get the quantitative answer. – John Alexiou Mar 20 '17 at 02:27