# Torque Simply Explained

## Important Formula

## What do the formula symbols mean?

## Torque

`$$ \class{green}{M} $$`Unit

`$$ \mathrm{Nm} = \frac{\mathrm{kg} \, \mathrm{m}^2}{\mathrm{s}^2} $$`

## Angular acceleration

`$$ \class{red}{\alpha} $$`Unit

`$$ \frac{\mathrm{rad}}{\mathrm{s}^2} $$`

## Moment of inertia

`$$ \class{brown}{I} $$`Unit

`$$ \mathrm{kg} \, \mathrm{m}^2 $$`

The **torque** \( \class{green}{\boldsymbol{M}} \) is defined as follows:

The torque is the cross product of **lever-arm length** \( \boldsymbol{r} \) and **force** \( \boldsymbol{F} \).

Because of the cross product the torque vector is always *perpendicular* to \( \boldsymbol{r} \) and \( \boldsymbol{F} \)! Its magnitude \( |\boldsymbol{r}\times \boldsymbol{F}| = \class{green}{M}\) is the area spanned by the vectors \( \boldsymbol{r} \) and \( \boldsymbol{F} \).

The magnitude of the torque, according to the definition of the cross product, is given by the following formula:

Here \(\varphi\) is the angle enclosed by the vectors \( \boldsymbol{r} \) and \(\boldsymbol{F}\). The torque becomes maximum when the two vectors are orthogonal to each other. So if the angle is \(\varphi = 90^{\circ}\). Formula 2

then simplifies to the product of the force and lever-arm length.