The unit of Torque

Question

Whenever we define a physical quantity, we know what 1 unit of that quantity tells us. For example, when we say 5 Pa, we're saying 5 N force acts perpendicularly on every unit area of the material but I've never been able to understand this for moment of force. What is 1 N$\cdot$m exactly telling me?

Answer 1

It is a 1 newton force applied at a radius of 1 meter, or its equivalent. For example two newtons force at a radius of 0.5 meters would also equal a 1 N$\cdot$m torque and so forth. Force times the radius it was applied at equals torque.

Answer 2

Well, 1 N$\cdot$m is when, 1 N of a force is applied at a point on the arm, which is at a distance of 1 m from its axis of rotation. So the torque generated under this condition is 1 N$\cdot$m.

Answer 3

5 Pa is a unit of pressure equal to $F/A$ and is a scalar quantity.

N$\cdot$m, when specified as a unit of torque, $\vec\tau$, is a vector quantity where

$$\vec\tau=\vec r \times \vec F$$ Where

$\vec F$ is the applied force

$\vec r$ is the position vector of the force relative to the point where the torque is calculated, and

$\times$ indicates the cross product of the two vectors. The magnitude of the torque is then

$$\tau=rF\sin\theta$$

where $\theta$ is the angle between $\vec r$ and $\vec F$.

That said, pressure can produce torque. If $\vec F$ is the total force associated with the pressure field and $\vec r$ is a vector from the center of pressure, where the total force can be assumed to act, and a point about which the torque is to be determined, the torque about that point is $\vec \tau=\vec r \times \vec F$.

Hope this helps.