Defining Torque: Why F*d? - 65 characters

[G01]

We define torque as a quantity that tends to cause rotational acceleration in an object and that:

$$\tau = F \cdot d$$

where d is the distance from the center of rotation.

My question is, why was it defined in this way in the first place?

It works, yes, but how did we know it'd work? Is it because toque is directly proportional to both d and f and the proportionality constant was experimentally proven to be 1? I was thinking there was more to it. Can someone please elaborate on this for me?

 

[Astronuc]

The definition of torque is based on the principle of levers.

http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalDynamics/DefinitionOfTorque.html

http://en.wikipedia.org/wiki/Torque

 

[Psi-String]

We define torque as a quantity that tends to cause rotational acceleration in an object and that:

$$\tau = F \cdot d$$

where d is the distance from the center of rotation.

My question is, why was it defined in this way in the first place?

It works, yes, but how did we know it'd work? Is it because toque is directly proportional to both d and f and the proportionality constant was experimentally proven to be 1? I was thinking there was more to it. Can someone please elaborate on this for me?

This also reminds me why rotational inertia is

$$\int r^2 dm$$

Is this just a mathematical conclusion or it has physical meaning?

 

[Cyrus]

Inertia is a 4th dimensional property. It is just mathematical. B.T.W that is the polar mass moment of inertia, not rotational inertia.

To G01,

it is defined this way because anything that is NOT EXACTLY perpendicular to the body will NOT cause ANY rotation. Therefore, ONLY that definition holds true. You see, it makes no sense to have a need for a proportionality constant. How will it help? If you try to do an experiment to measure the torque, how will you measure the amount of torque? By using your equation you defined torque to be that's how! See my point? You can't just go and measure torque without first saying, this is what I will call torque.

Edit: Well,I guess one way you could verify it is if you put a torque on a wheel, and from that you can measure its angular acceleration, which would be a measurement independent of the definition of torque. From there, you should see values that match your equation, *if* your initial assumption of torque being t=fd was correct.

 

[Astronuc]

Inertia is a 4th dimensional property.

More precisely, inertia is the 4th moment of a mass distribution.

 

[Cyrus]

Not to my knowledge, its called the 2nd moment about an axis astronuc. Its a 4th dimensional property.