How does torque even work on intuitive level? I just watched some videos on torque, and that created confusion in me.

*

*What exactly is torque?!
Some people say it is the rotational equivalent of a force, but the units do not match out. Some say it is the twist of a rigid body. But that again is force. Some say it is the turning effect of force, but does that mean that torque is the effect of the application of force?. Some say that torque is the ability of a force to cause angular acceleration, but even force has that ability, and this statement says that torque is the ability of an ability to cause motion, and so we are saying that torque=type of force, but units??

*what is meant by 1Nm of torque? Does that mean that there is 1N of tangential force 1m from the pivot point of a rigid body? Why the heck does this even be useful? What does it tell us about the body?

*what does the application of torque even mean?
4)is there any intuitive reason for why the distance thing from the pivot is a factor on which torque depends apart from the formula or experiments?

*why does this velocity decrease if there is an increase in torque for a constant power output? (please DO NOT use the formula, I know inverse relations-please give an intuitive reason), since when there is more torque, there is more force at that particular distance, so there must be more acceleration, so more velocity. How does this work?
I have many more questions, but I dont know how to put them. Please help.

 A: (1) Torque is defined as $\vec{M} := \vec{x} \times \vec{F}$, indeed it is NOT a force, but it has some analogy to it since it satisfies the equation
\begin{equation}
\frac{d\vec{L}}{dt} =\vec{M}
\end{equation}
which is somewhat similar to Newton's equation for force and momentum.
(2) It means exactly what you you wrote, assuming you mean normal by tangential.
(3) Torque gives you the time derivative of the angular momentum of a body. I believe in physics experiments are intuition, whether they are mental experiments or not, so i dont know of a way to give intuition without experiments
(4) Not exactly sure of the situation you mean
A: If you want to tighten a nut on a bolt, you can do it either with a short spanner and a large force from your hand (on the end of the spanner), or by using a long spanner and you will only require a smaller force from your hand.
If you want to drive a tractor across a muddy field, you can either apply a very large force to the teeth of a small cog on the axel, or a smaller force to the teeth of a larger cog.
If you want to open a door then you can either push with a moderate force somewhere near the handle, or you can try pushing somewhere near the hinge, but then you will need a much larger force.
Finally, if from Newton's second law we have
$$
{\bf f} = \frac{d {\bf p}}{dt}
$$
and we define the quantity
$$
{\bf L} = {\bf r} \times {\bf p}
$$
for a point particle at position $\bf r$ with momentum $\bf p$, then
$$
\frac{d \bf L}{dt} = \frac{d \bf r}{dt} \times {\bf p}
+ {\bf r} \times \frac{d \bf p}{dt}
= {\bf r} \times {\bf f}.
$$
This is useful because the sum of $\bf L$ over the parts of an isolated system is not changed by the action of forces internal to the system (this is called conservation of angular momentum). So angular momentum is a useful quantity. When an external force acts the rate of change of the angular momentum is given by the ${\bf r} \times {\bf f}$ so that quantity also gets a name: torque.
A: *

*A force can cause different rotations.

*A torque can only cause one rotation.*

So, if I tell you a torque that is being applied by a wrench, then you right away know the resulting rotation it causes. If I just tell you the force, then you can't know yet. You don't have enough information.
Because apart from the force you also need to know the angle and distance from the point of rotation. Torque is invented to include all this into one single property.
Torque is the rotational equivalent of force in the same way that angular acceleration is the rotational equivalent of linear acceleration. You could say the same for, say, moment-of-inertia and mass. The units don't have to match for there to be an equivalence - only for there to be an equality. And noone is claiming them to be equal - just equivalent in an intuitive sense.
This was an answer to your question 1). Let me know if this clarifies the initial doubts.

* Assuming everything else constant. Rotation could be represented e.g. by angular acceleration.
A: The best definition of torque is the work per unit angle of rotation (as in Joules/radian) that can be done by a force which is acting in a maner that might cause a rotation. This can be shown to be consisent with the various fomulas.  To do work, you want the component of the force which in the direction of motion along an arc. The work would be that component times the arc length Rθ.  Multiply by F and divide by θ and you get τ = FR.
