Understanding Classical Torque

[BBRadiation]

I am having a difficult time understanding the reasoning behind torque. From a textbook I read,

"A doorknob is located as far as possible from the doors hinge line for a good reason. If you want to open a heavy door, you must certainly apply a force; that alone, however, is not enough. If you apply your force nearer to the hinge line than the knoe, or at any angle other than 90, to the plane of the door, you must use a greater force to move the door than if you apply the force at the knob and perpendicular to the door's plane."

However, why is it that it's easier to rotate a door when you are farther from the rotational axis? You are still moving the same amount of mass. Of course, I know that torque = r x F and thus increasing r decreases F if you are to maintain the same torque. But why is this true? What property of the object rotating explains this?

Thanks

 

[Jasongreat]

It seems to me that although you are moving the same mass(the door) from both positions, when you are closer to the hinge you have to move that mass over a shorter distance, more force per inch. When farther away you have to move the same mass but over a greater distance, so it takes less force per inch, making it easier.

 

[russ_watters]

It's mechanical advantage via a lever: http://en.wikipedia.org/wiki/Lever

 

[BBRadiation]

It's mechanical advantage via a lever: http://en.wikipedia.org/wiki/Lever

Right, I know that. But why does mechanical advantage occur is what I am trying to get at.

 

[russ_watters]

I'm not sure there is a "why" (there typically isn't, in science) other than if it didn't, there'd be unbalanced forces and no conservation of energy.

 

[K^2]

There is derivation on this page. Rigid Body Dynamics. It derives torque as consequence of Newton's Second Law. Maybe it will help.

 

[quantum123]

I think he is asking for a physical intuitive explantion and not a vector analysis type of explanation.
I think you have to go back to elementary science where torque is called moment, and even before that, it is called turning effect.
Sure you can apply a force anywhere, but it is not the same effect if you change your point of application.
That is why there is such a thing called leverage, or mechanical advantage. As in a crowbar, you can carry an elephant using your pinkie, provided you have a sufficiently long rod.
;)
ps One possible explanation that why this mechanical advantage has to occur is : the conservation of energy.

 

[BBRadiation]

I think he is asking for a physical intuitive explantion and not a vector analysis type of explanation.
I think you have to go back to elementary science where torque is called moment, and even before that, it is called turning effect.
Sure you can apply a force anywhere, but it is not the same effect if you change your point of application.
That is why there is such a thing called leverage, or mechanical advantage. As in a crowbar, you can carry an elephant using your pinkie, provided you have a sufficiently long rod.
;)
ps One possible explanation that why this mechanical advantage has to occur is : the conservation of energy.

Yeah, I am looking for the physical intuitive explanation. Could you possibly expand on the idea of conversation of energy as a reason for mechanical advantage?

Thanks

 

[jambaugh]

A torque is in units of force times distance, more precisely F x r (cross product).
So you can increase torque by increasing the force or increasing the lateral distance.

It helps to think of torque in terms of coupled forces. I.e. for 1 Newton-meter apply half a Newton of force at two points, equally spaced 1 meter from an axis (like turning a 1m radius steering wheel.)

If you need more elaboration consider how work is done e.g. force times distance.

Torque is the generalized force associated with rotation so angular work is done by torque times angle (in radians).

Thinking then in terms of resolving a rotationally applied force, since the distance a point travels during a rotation is angle times radius:
$$s = r\cdot \theta$$
Work is then:
$$F \cdot s = F\cdot r \cdot \theta = \tau \cdot \theta$$

So force times radius is a natural angular force to give the same amount of work done and that is torque.

That is for magnitudes but once you understand that you can work with the vector form.

It pays to work through all the usual linear formulas converting them to angular form.
work = force times distance (above)
force is time rate of change of momentum (torque is time rate of change of angular momentum)
force = mass times acceleration (torque = moment of inertia times angular acceleration.)

 

[quantum123]

Think of a crowbar, the work you do (energy input) = the increase in PE of the stone you lift.
Large force X small distance = small load X large distance.
You need to move a lot just to move the heavy stone a little, because energy is conserved.

This is just one explanation.