My name is Alexander FufaeV and here I write about:

# Rolling Motion

## Important Formula

## What do the formula symbols mean?

## Total energy

`$$ W $$`Unit

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

Total energy of a rolling body is composed of the rotational energy and the kinetic energy of the translational motion.

## Velocity

`$$ \class{blue}{v_{\text c}} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Linear velocity of the center of mass of the body. This velocity indicates how fast the body is rolling.

## Mass

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

`$$ \mathrm{kg} $$`

Total mass of the rolling body.

## Moment of inertia

`$$ I_{\text c} $$`Unit

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

Moment of inertia for an axis of rotation passing through the center of mass of the body.

## Angular velocity

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

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

The angular velocity indicates the angle covered per time, that is how fast the body rotates.

Rolling motion refers to the type of motion that a cylindrical or round body performs on a surface as it moves forward by rolling about its own axis. Unlike sliding motion, in which a body glides over a surface, a rolling body actually rotates about its axis as it moves forward.

$$ \begin{align} W ~=~ \frac{1}{2} \, \class{brown}{m} \, {\class{blue}{v_{\text c}}}^2 ~+~ \frac{1}{2} \, I_{\text c} \, \class{red}{\omega}^2 \end{align} $$