Question

In F=ma when summing the forces, I know they must all be in the same direction (along with the acceleration), but should they all be acting on a single point also (or acting relative to a point)?

So if you had two forces acting on an object and say one is acting on the center and one is acting on some distance from the end, you must set up an origin point, and have two position vectors from the origin to the each of the forces. The result would then be the force times this distance (and whatever trig is needed to break the force it into appropriate components) summed with the other force times its distance and possibly whatever trig (again to break the force up), if needed. Resulting in basically a torque equation?

(I don’t know if this is correct, it’s just my guess that this would be the process if it’s true F=ma is for forces on a single point, or must be acting relative to something).

If it is true though, and you have to incorporate this distance making it seem as though it’s torque, where does the fact that it should be the perpendicular distance from the origin (or in the case of torque a “pivot point”) come into play? I know intuitively that you cannot turn or twist something if you push parallel to a pivot point, but I’d like to have a better understanding of that.

Thank you !

Answer 1

Your intution is absolutely correct. But mathematically you need sin component with respect to the r vector. As the torque is defined as the cross product of f and r so it leads to the sin component. Because of the cross product the sin component of force and r become perpendicular. To generate a torque you need a pivot point otherwise the object will perform translational motion instead of rotation.

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