# Equilibrium of a body in torque problem

I was watching a video about torque in which the task was to find the force $$F_2$$ when a body is in equilibrium. The person in the video said that in order for the body to be in equilibrium, two things must happen: a) the net force must be zero, and b) the net torque must be zero.

Now, when solving the problem, he wrote that

net force = force $$F_1$$ + force $$F_2$$ + force of reaction ($$F_1$$ and $$F_2$$ were forces acting on the body)

net torque = torque1 + torque2 + torque of the reaction force

Investigating a bit more, I learned that there are two types of equilibrium: translational and rotational. In the video they didn't specify which one they meant, but I'm guessing it was both since we're taking both net force and net torque into account.

What I don't understand is why the reaction force is used here. I thought that translational equilibrium happened only when the net force ACTING ON a body is zero. But the reaction force is not a force acting on the body, it's a force being exerted by the body. In the same way, rotational equilibrium is when the net torque acting on the body is zero.

So why is the reaction force relevant? Is the person in the video wrong, or should we use the reaction force for calculating the net force and net torque? This was the situation presented:

According to my interpretation, it's not possible for that object to be both in translational and rotational equilibrium at the same time.

• You haven't said what your system actually is, so no one can tell you what that reaction force is. – Aaron Stevens Jul 14 '19 at 11:32

The reaction force is just the force according to Newton's 3rd law, it should have the opposite sign to the force that causes the reaction. The reaction force can be caused by linear inertia, moment of inertia (rotational inertia) or another object. Since there is only one object on your diagram - it is the former. The reaction force caused by inertia is a force that is generated by the body, thus it is an internal force.

You are correct in the other regard - In order for a body to be in rotational equilibrium, the vector sum of the forces acting on that body, must lie on a line that passes through the body's center of mass.

• So in the problem I showed in my post(the image), there is a reaction force, right? But what causes the reaction? That's what I'm struggling to understand. I don't know what that force comes from. I think only two forces are acting on object, but I heard from the video that there's also a reaction force. – Agus Jul 14 '19 at 1:36
• The reaction force can be caused by linear inertia, moment of inertia (rotational inertia) or another object. Since there is only one object on your diagram - it is the former. I have added this info to my answer. If it is useful to you - vote it up. – George Robinson Jul 14 '19 at 10:03
• Take a look at the Question at bit.ly/2XR3UNr This Question is relevant because it shows what must be done in order for a floating object to be in a rotational equilibrium. Don't forget to vote if you like this question and its diagram. – George Robinson Jul 14 '19 at 10:23
• I don't understand what you mean by saying the force comes from linear inertia. Inertia isn't a force. – Aaron Stevens Jul 14 '19 at 11:32
• ...but inertia of the body provides resistance to the external force. That resistance provides an equal but opposite reaction force (created by the body's inertia), according to Newton's 3rd law. – George Robinson Jul 14 '19 at 20:03

But the reaction force is not a force acting on the body, it's a force being exerted by the body.

By Newton's third law if the body is exerting a force onto "something" then a force equal in magnitude and opposite in direction is being exerted onto the body by the "something"

For example, think of a car on the ground. The car pushes into the ground, so the ground pushes up on the car.

In your example you have not said what your system is, so I can't say where this force actually comes from physically. Usually it's a normal force of some kind that results from electrostatic repulsion. It's the same force you would feel if you tried to push your hand through a table.

Translational equilibrium means that the center of mass of an object feels no force to accelerate it to some direction.

The rotational equilibrium means that an object didn't rotate.

Both of them are fulfilled for every fixed, non-moving thing.

For example, a properly built house will neither give way under it, nor will fall down by rotation.

Reactive forces act on a body as a result of acting of the body to other objects. The matter of your confusion is probably in the idea that in

net force = force $$F_1$$ + force $$F_2$$ + force of reaction (F1 and F2 were forces acting on the body)

you unconsciously connected the term “force of reaction” with forces $$F_1$$ and $$F_2$$. No, force of reaction is an other force — the force “returned” to the object from an other object.