# How does torque differ from force?

Jun 10, 2014

Force is a vector (applied in a straight line, with the acceleration in the same direction as the net force).

Torque $\setminus \vec{\tau}$ refers to applying a force $\setminus \vec{F}$ to a lever arm at a specific distance $\setminus \vec{r}$from the center of rotation.

$\setminus \vec{\tau} = \setminus \vec{r} \setminus \times \setminus \vec{F}$

You push your car with a force, but you apply torque to the lug nut to loosen it in order to change your tire. With torque, you talk about force at a distance, and angular acceleration instead of linear acceleration.

Force has units of Newtons, while torque, being the product of a force and a distance, has units of Newton$\setminus \cdot$meters.

Torque and force also differ in that force is a true vector, whereas torque is a pseudovector, that is, it picks up a sign flip under certain kinds of coordinate transformations.

In terms of derivatives, force is the time derivative of the linear momentum:
$\setminus \vec{F} = \setminus \frac{d \setminus \vec{p}}{\mathrm{dt}}$
while torque is the time derivative of angular momentum:
$\setminus \vec{\setminus} \tau = \setminus \frac{d \setminus \vec{L}}{\mathrm{dt}}$