Why a greater torque causes an object to rotate

[aaaa202]

Okay, a few days ago I posted a question about torque, and recevied A LOT of useful help on understanding the term. I however must admit, that I still don't quite have the intuition behind why a greater torque causes an object to rotate faster.
THEREFORE: Can someone with logical, physical arguments explain why a force exerted farther away from the rotational centre causes a bigger angular acceleration than one exerted on a body closer to the rotational centre. This argument must not refer to the term torque, since it is torque as a whole that I wonna get the intuition behind.
I was suggested to use an energy observation, that since an angular displacement means bigger work the farther you are from the axis of rotation you get more kinetic energy, but thought this wasn't valid since a force is something instantaneous and doesn't necessarily have to act over time.
Therefore clever physicists, give a young student some intution for the important idea of torque..

 

[NascentOxygen]

Can someone with logical, physical arguments explain why a force exerted farther away from the rotational centre causes a bigger angular acceleration than one exerted on a body closer to the rotational centre.

Think of some device you have used, where it has a handle to rotate a body. This could be a cement mixer, an emery wheel (grind stone), a kitchen mincer, etc. (Failing this, maybe consider a playground hurdygurdy merry-go-round thing. You stand a couple of children on it, tell them to hang on tight, then you run around the outside trying to spin it faster and faster but eventually making yourself so dizzy that you give up and fall over.)

For something with a handle, if you move the point of application of the force (the handle) further out from the centre, then you don't need to exert as great a force to make the body rotate at the same speed as before. That is, if you double the distance out, you halve the force required.

But if you have extended the handle out from the centre, then you'll find you have to move your arm further & faster in order to apply that same force, for if you don't, then the handle outpaces your hand. And you can't apply a force if your hand can't even keep up with the handle.

Now, let's minimise friction, so the force you exert causes the rotating body to rotate at ever increasing speed. If you extend the radius where the force acts, but try to maintain the same force, you are going to have to make your arm travel faster. Since your arm matches the speed of the rotating body, this is another way of saying the body is going to rotate faster and faster than before. If your hand does not move faster, the handle will outpace your hand and you'll have nothing to push against. If you have nothing to push against, you can't be exerting a force.

 

[rcgldr]

I was suggested to use an energy observation, that since an angular displacement means bigger work the farther you are from the axis of rotation you get more kinetic energy, but thought this wasn't valid since a force is something instantaneous and doesn't necessarily have to act over time.

The assumption is that the force is continously applied. If there's no friction and only angular momentum, then as posted above, in order to generate the same force at a larger radial distance from the center of the rotating object, that force has to be applied at a greater rate of acceleration. This tranlates into that force being applied at a greater speed at any moment in time (other than the initial angular speed of zero), which translates into a greater amount of force x distance over any period of time, which represents a greater amount of work done and a greater amount of angular energy added to the rotating object.

 

[aaaa202]

fantastic, I never thought of looking that way at it. Thanks to you both :)

 

[aaaa202]

Buuuuut.. I thought about a little more now, and came to the conclusion that you're way of looking at it works, when our torque actually causes a rotation.
But truth is that torque is also applicable for equibrilium situation in which we have to find out how to apply 2 forces such that the object does NOT rotate.
For example.
If we apply 10N 1m away from the center of mass of a rod and need to find out where to apply 5N such that it does NOT rotate, we see that the force must be exerted 2m away.
So what would you say in this situation? Maybe I just have to accept that torque is quite abstract and hard to understand without an intuitive approach to how objects in our everyday behave. The same can namely be said about a force and a torque is after all the rotational analogue to that..

 

[NascentOxygen]

If we apply 10N 1m away from the center of mass of a rod and need to find out where to apply 5N such that it does NOT rotate, we see that the force must be exerted 2m away.
So what would you say in this situation?

If you can appreciate the principle of the child's see-saw, then you can understand this.

There's a see-saw in the park, and there's a small kid sitting on the end of it. His fat brother wants to sit on the other end, so you place the heavier boy in closer towards the fulcrum so the see-saw can still balance. (This makes the torques approximately equal, so the see-saw stands a chance of balancing.)

 

[aaaa202]

Yeah okay.. But that was not a physical argument - rather an intuitive one :)

 

[A.T.]

it is torque as a whole that I wonna get the intuition behind.

But that was not a physical argument - rather an intuitive one :)

Didn't you want to get an intuitive understanding?

https://www.youtube.com/watch?v=Sm4pV3xyJRE

Otherwise I don't understand what you want to hear. Torque is an abstract concept, just like forces, energy... etc.. The reason why they all are defined as they are, is: Because that definition turns out to be useful.. Torque was defined such that zero angular acceleration means zero net torque, in the same way that force was defined such that zero linear acceleration means zero net force.