Where does the torque force come from?

Question

If there is an object which is $10 kg$, and we apply a force $|\vec F| = 100N$ then it will accelerate in the diraction where the force vector points with $10 m/s^2$

If the mass center is at point $O$ and the force is applied at point $P$, then the object will also have some radial acceleration $\tau=F|OP|$

What I do not understand, is that if all the force is converted to linear acceleration, then where does the radial acceleration come from?

I don't know if I am getting the whole picture of the problem here, but I guess you are considering 2 different separate cases, in one you are at an observer's inertial frame and the other one considers the center of mass frame. By Varignon's theorem, there are some quantities called "strains" that are applied as forces towards radial vectors along a surface or a line of action, and the sum of all of them along all the points equals the total force. — omivela17, Jun 29 '18 at 18:44
Isn't the linear acceleration independent from the location where the force was applied on the object? — Iter Ator, Jun 29 '18 at 18:46
I try to imagine, the effect of a thruster on a spaceship ( in 2D for simplicity ) — Iter Ator, Jun 29 '18 at 18:52
These "strains" or "torques" I mention are not forces, but vectors. You can see by analysis of units that $[\tau]\neq[F]$. — omivela17, Jun 29 '18 at 18:53
Possible duplicate of If I push or hit an object in space will it rotate or move along a straight line? — V.F., Jun 29 '18 at 19:22
Some very good answers to a similar question in this post: https://physics.stackexchange.com/q/235482/ — V.F., Jun 29 '18 at 19:22

score 0 · Answer 1 · answered Jun 29 '18 at 19:12

Force is not a conserved quantity, but energy is. It must be that more energy is used when the force is applied off the center of mass rather than on it. However, this is curious. Suppose you have two thrusters on this spaceship opposite the center of mass. When you burn them, the ship won't move at all, nor rotate. So we must conclude that the energy from the thrusters is lost as heat. But now move each thruster to the left and right of the center of mass. If the ship has the right symmetry, it still won't gain any linear momentum, but it will rotate. That means some of the energy from the thrusters become rotational kinetic energy, while the remainder is lost as heat. Finally, point both thrusters in the same direction to one side of the center of mass, and the ship will move and rotate, so the energy from the thrusters becomes linear kinetic energy, rotational kinetic energy, and heat. So is the amount of heat dependent on where the thrusters are fired? I suppose so, but I'm not sure exactly how that works out.

score 0 · Answer 2 · answered Jul 16 '18 at 23:46

Force, linear acceleration, and linear momentum are all related to each other.

Torque, angular (rotary) acceleration and angular momentum are related to each other.

But the two groups are separate.

When you apply an unbalanced torque on an object, it'll change its rotation. That's about torque, not about the force(s) that make up that torque.

A force isn't "used up" when it's part of a torque and vice-versa. Force and torque are separate concepts, separate things.

Where does the torque force come from?

2 Answers2